You're not giving Davis much credit for figuring out what he should and shouldn't admit at a time when foreign recognition of the Confederacy was such a critical issue. But here's what Davis said about the Mississippi Declaration of Secession (where they stated that "our position is thoroughly identified with slavery") when he resigned from Congress:
"...if I had thought that Mississippi was acting without sufficient provocation, or without an existing necessity, I should still, under my theory of the Government, because of my allegiance to the State of which I am a citizen, have been bound by her action. I, however, may be permitted to say that I do think she has justifiable cause, and I approve of her act. I conferred with her people before that act was taken, counseled them then that, if the state of things which they apprehended should exist when their Convention met, they should take the action which they have now adopted...
It has been a conviction of pressing necessity -- it has been a belief that we are to be deprived in the Union of the rights which our fathers bequeathed to us -- which has brought Mississippi to her present decision. She has heard proclaimed the theory that all men are created free and equal, and this made the basis of an attack upon her social institutions; and the sacred Declaration of Independence has been invoked to maintain the position of the equality of the races. That Declaration is to be construed by the circumstances and purposes for which it was made...They have no reference to the slave...we find provision made for that very class of persons as property; they were not put upon the equality of footing with white men -- not even upon that of paupers and convicts; but, so far as representation was concerned, were discriminated against as a lower caste, only to be represented in the numerical proportion of three-fifths. So stands the compact which binds us together."
And here's what Davis said in his first message (delivered on April 29, 1861) to the Confederate Congress:
As soon, however, as the Northern States that prohibited African slavery within their limits had reached a number sufficient to give their representation a controlling voice in Congress, a persistent and organized system of hostile measures against the rights of the owners of slaves in the Southern States was inaugurated and gradually extended. A continuous series of measures was devised and prosecuted for the purpose of rendering insecure the tenure of property in slaves. Fanatical organizations, supplied with money by voluntary subscriptions, were assiduously engaged in exciting amongst the slaves a spirit of discontent and revolt; means were furnished for their escape from their owners, and agents secretly employed to entice them to abscond; the constitutional provisions for their rendition to their owners was first evaded, then openly denounced as a violation of conscientious obligation and religious duty; men were taught that it was a merit to elude, disobey, and violently oppose the execution of the laws enacted to secure the performance of the promise contained in the constitutional compact; owners of slaves were mobbed and even murdered in open day solely for applying to a magistrate for the arrest of a fugitive slave; the dogmas of these voluntary organizations soon obtained control of the Legislatures of many of the Northern States, and laws were passed providing for the punishment, by ruinous fines and long-continued imprisonment in jails and penitentiaries, of citizens of the Southern States who should dare to ask aid of the officers of the law for the recovery of their property. Emboldened by success, the theater of agitation and aggression against the clearly expressed constitutional rights of the Southern States was transferred to the Congress; Senators and Representatives were sent to the common councils of the nation, whose chief title to this distinction consisted in the display of a spirit of ultra fanaticism, and whose business was not "to promote the general welfare or insure domestic tranquillity," but to awaken the bitterest hatred against the citizens of sister States by violent denunciation of their institutions; the transaction of public affairs was impeded by repeated efforts to usurp powers not delegated by the Constitution, for the purpose of impairing the security of property in slaves, and reducing those States which held slaves to a condition of inferiority. Finally a great party was organized for the purpose of obtaining the administration of the Government, with the avowed object of using its power for the total exclusion of the slave States from all participation in the benefits of the public domain acquired by all the States in common, whether by conquest or purchase; of surrounding them entirely by States in which slavery should be prohibited; of thus rendering the property in slaves so insecure as to be comparatively worthless, and thereby annihilating in effect property worth thousands of millions of dollars. This party, thus organized, succeeded in the month of November last in the election of its candidate for the Presidency of the United States.
In the meantime, under the mild and genial climate of the Southern States and the increasing care and attention for the well-being and comfort of the laboring class, dictated alike by interest and humanity, the African slaves had augmented in number from about 600,000, at the date of the adoption of the constitutional compact, to upward of 4,000,000. In moral and social condition they had been elevated from brutal savages into docile, intelligent, and civilized agricultural laborers, and supplied not only with bodily comforts but with careful religious instruction. Under the supervision of a superior race their labor had been so directed as not only to allow a gradual and marked amelioration of their own condition, but to convert hundreds of thousands of square miles of wilderness into cultivated lands covered with a prosperous people; towns and cities had sprung into existence, and had rapidly increased in wealth and population under the social system of the South; the white population of the Southern slaveholding States had augmented form about 1,250,000 at the date of the adoption of the Constitution to more than 8,500,000 in 1860; and the productions of the South in cotton, rice, sugar, and tobacco, for the full development and continuance of which the labor of African slaves was and is indispensable, had swollen to an amount which formed nearly three-fourths of the exports of the whole United States and had become absolutely necessary to the wants of civilized man. With interests of such overwhelming magnitude imperiled, the people of the Southern States were driven by the conduct of the North to the adoption of some course of action to avert the danger with which they were openly menaced."
As the Mississipians and the other Confederate states openly acknowledged in their declarations of secession, their position was indeed "thoroughly identified with slavery."