Davy Crockett didn't. That was a lie propragated 70 years after Crockett's death by the Whig party. Crockett never made the speech "Not mine to give" to congress or it would have been recorded in the Congressional annals. Crockett actually voted on several bills to provide help to individuals and his voting record was mixed on the matter. He considered each case individually.
I'm not sure you are correct on this. Though I didn't spend the time going through Congressional records, I found there is much support that Davy Crockett did make this so-called "Not mine to give" speech. I went on line and searched "Not mine to give Crockett" and came up with many sites that support it; and none that refute it. Please give a site that refutes it.
Not to be pedantic, but Crockett died in 1836. Seventy years later gets us to 1906 -- I'm not sure if the Whig's were very active then, spreading lies or doing much of anything.