Yeah, secret in 1836. Lincoln spoke in 1846 by which time the treaties were already entered records. That he premised his speech on the wrong half of the treaty indicates either gross ignorance or willful deception on his part. That would make Lincoln either a fool or a liar - I'll let you pick which one.
And here's what the Texas State Library site you linked to says about it
I'm amused at how willing you are to take your history lessons out of the unsourced snippets of a bureaucracy, but what we do know of the 1840's indicates that Texas very much so considered the treaty to be valid and binding. Polk's speech treated it the same, referencing the Rio Grande boundary stipulation. The only people who seemed to have an issue with it at the time were, obviously, the invading Mexicans and those giving them aid and comfort in the minority party of Congress, among them Lincoln.
Which is exactly Lincoln's point in the speech. Just saying that you own your neighbor's property doesn' t make it so unless your neighbor agrees. Mexico never accepted the treaty.