Yes, you did state the belief Thomas Sr. is from Ireland is unsourced, and has come down in your family by word of mouth. That much is undeniable. It's well known to genealogists, those who actually do research, that the lengend is unproven, and unsupported, the belief in it is unshared by the majority of family members, and it's been denied, or doubted, by some family members ever since its thought to have first surfaced.
In addition though, you also stated, "There has neverbeen a question in our family (the family with whom the legend seems to have originated.) that our Culwell line is originally of Irish descent.", and "I believe Thomas, or the generation prior to Thomas. did immigrate here from Ireland.".
As long as the legend had been neither proven, nor disproven, it could be presented as perhaps a possibility to be considered, and remaining to be either proven, or disproved, but certainly no more than merely that. That changed though when it was found two of Thomas's sons had testified he was not born in Ireland. This is documented firsthand testimony from people who knew him personally and knew him well. It constitues proof he was not born in Ireland, and the legend, as is true of most legends, has apparently no basis in fact.
I'll add that in your last posting, you said, in reference to your belief in the legend, that while you can find no evidence to substantiate it,"... neither is there any proof or documentation to prove otherwise.". I'm sorry, but by the rules and standards of genealogical research, the documented testimony of two of Thomas Sr's sons is proof he wasn't born in Ireland. You're right in saying you shouldn't blindly accept the results of other people's research, but it's easy enough to check the 1880 census, and see for yourself what Thomas's sons said.
I don't deny, because I can't deny, that maybe somebody confused the generations, and perhaps Thomas Sr,'s father was from Ireland. I can't deny it because we don't know where he came fom, and so he could possibly have come fromanywhere! Given what we don't know, I couldn't deny that he could possibly have come from Yugoslavia!
You'll believe what you want to believe, for whatever reasons, that to you, validate your belief. If it's only that your family members have always believed it, then so be it. You're entitled to your beliefs, and entitled to share them if you want to. It doesn't really matter what you believe, or what I believe either, and where Thomas was born is really of no importance whatsoever. If he'd been an Eskimo, it would change nothing.
What I'm concerned with is that the internet is full of people who don't know, and can't tell, the difference between actually doing research, and merely collecting the results of other people's research. They'll believe anything, and everyting, they see in print, and without verifying any of it, will pass it on to others as fact. Warning them that a legend is unproven makes no difference. If they like it, they'll report it as though fact anyway, and then it spreads. If we're interested in compiling an accuarate history of the family, it's best, I think, that we be very cautious in reporting legends, or assumptions, on the net. For the inexperienced, the internet is genealogical quicksand!
I'm going to now write again. We are cousins, and I hope we'll become friends. I don't care where Thomas Sr. was born, and I don't care who believes what. I care only that in doing research, we abide by the rules, and that requires us to accept as fact that the documented testimony of two of Thomas's sons, saying he wasn't born in Ireland, constitues proof he wasn't born in Ireland.