before Lincoln issued the Emancipation Proclamation, Jefferson Davis freed all the slaves in the south.

Ahahaha holy shit no. Jefferson Davis did not at any time free the slaves in the South. In fact, chapters 51 and 52 of Davis's history of the Civil War, The Rise and Fall of the Confederate Government, concern themselves with the Union occupations of confederate states, and how, specifically, slaves in each of those states were declared free. Whether by military commander or by act of (Union Controlled) state legislature. Davis never thinks to mention that this was all pointless, as he had freed the slaves already. Davis however, does make it very clear what his opinion of freeing the slaves was.

[union armies freeing slaves] violated all the principles of the law of nations, without a shadow of authority for it under the Constitution of the United States. The armies of the United States were literally authorized to invade the Confederate States, to seize all property as plunder, and to let the negroes go free. Our posterity, reading that history, will blush that such facts are on record. It was estimated on the floor of the House of Representatives that the aggregate amount of property within our limits subject to be acted upon by the provisions of this act would affect upward of six million people, and would deprive them of property of the value of nearly five thousand million dollars.

So even is Davis was opposed to slavery (which he absolutely was not) he certainly would not have considered it a good idea to deprive his citizens of five billion dollars in 1864 money during the middle of a war.

Is there anything that would support this claim?

I mean no, the closest thing I could think of would be various proposals floated near the end of the war, when it was clear that the South was losing, that slaves could be armed and persuaded to fight in return for their freedom. Freeing slaves was controversial, and arming them was almost more so. But in the end, the confederate congress passed a bill authorizing the arming of slaves, who would fight and die in return for....not being freed. it wasn't a very good bill, and Richmond was captured three weeks later, rendering the whole point moot.

If not, what would lead someone to believe this as fact?

I can't read your relatives minds, but Southerners have spent an awful lot of time and ink trying to avoid the rather obvious fact that the Civil War was about slavery. That I've been referencing, Jefferson Davis' thousand page history of the Civil War, should give you a pretty good idea how incorrect the "winners write history," chestnut is when applied to the Civil War.

In fact with the possible exception of Vietnam, I can't think of a war where the losers wrote more history. "Jefferson Davis freed the slaves," is a particularly brash bit of pro-confederate nonsense. But it fits roughly in the same genre as "Black confederates totally existed," "The war was actually about Federal versus State governments" "The war was about unequal tarrifs*", and "Life as a northern factory worker was totally worse than live as a southern slave." Which is to say, they are lies people tell to try to convince themselves their ancestors didn't fight and die for an evil and inhumane cause.

*This one goes back at least to, again, Jefferson Davis' history of the civil war.

Edit: Mods please let me know if this answer is too flippant, and I'll edit it down.