OK now i think I see where your coming from. True, Scots are mentioned by Romans earlier than the irish invasions of Scotland but Scot means "raider". The Romans where referring to raiders from north of Hadrians wall, not the specific group of raiders that came from Ireland, expanded Dal Riodha and became the Kingdom of Scotland. The earlier use of the word (meaning Raider) realy is a tenuous reason to doubt Irish and Scottish historical records, dozens if not hundreds of history books, Websites and the fact that Scots are undoubted Gaels just like the Irish. Where else could these Gaels have come from? The tribes who existed in Scotland during the Roman invasions were Brythonic Celts not Gaelic. The Kingdom of Dal Riodha was Gaelic, was Irish. There are clear differences between Gaelic and Brythonic Celts, we have a different language for a start.
Right for the sake of agument lets just say that the Scotti mentioned as existing in Scotland were the same tribe as those who later ruled Dal Riodha and not just different groups labeled "Scotti" (raiders) by the Romans. They what fight the Romans, cross the sea set up a kingdom in Ulster and then come back to Scotland as Dal Riodhans? This seems highly suspect but if we assume its true, by the time the cross back into Scotland they have changed from Brythonic Celts to Gaels, culturally, Linguisticaly. The changes they've gone though as an Irish kingdom have obliterated any trace of who they were before they came to Ireland. I a very real sence they have come from Ireland even if Geneticaly they were originaly from Scotland. And despite changing language, customs culture and all their personal names, they have clung on to the tribal name Scots. How is this a more logical explanation than the Romans naming 2 groups of raiders sparated by centuaries as "raiders"? When the spanish "discovered" the new world they called the natives Indians. Does this mean that Apache originated in the Indus valley?
There is a huge weath of evidence, historical records, genealogical, archaological, to support the idea that the Scots originated in Ireland. Their culture and language is not related or influenced to Gaelic, it is Gaelic. Tartan, whiskey, bagpipes, blue woad, claymores, clan and first names, placenames, attitude to life, attitude to the english, music, sectarian problems are all the same. Even after over a thousand years of separate evolution, we are still uncannily similar, still identifiably Gaelic. I could speacK irish gaelic to a scot and be understood. A few words and pronunciations would be differnt but no more different than if I spoke to a Kerryman. In fact i find scottish accents easier to understand than a Kerry accent. This is a lot to ignore for the sake of one word.
I have heard theories saying Scots were picts, Arthurian Britons, even Anglo-saxon, but without any convincing arguements to back this up. Hell, i'd love to believe that the Scots came from somewhere other than Ireland. It would mean Gaelic culture was more widespread than we think, that there were more like us but it would take a lot more to convince me than a single word. It just means Raider. If it were a tribal name that came from a root hero ( Eogannachta, Connachta ) rather than a description (scot\raider or Sennone\old-ones or veterans) then maybee that woulr imply something. But not when it means Raider, its too vague.
Type scottish history into a search engine, pick up a history book and you'll see im not the only one whos certain that the Scots came from Ireland.
I love disscussing Celtic history and the origins of my people. If you have any more evidence to say they might not be of Irish origin, please share. I'll happily admit I'm wrong if it means I learn more, I certainly don't know everything about my history, no-one does. For example I didn't know Scottish Cranogs where quite that old, thanks I sit corrected. But sorry, doubting Scottish origins over the use of as general a word as Scot is just way too much.
Hope to hear more

Tathy