It's not like Tyrion has been teaching her anything special on this subject, or that Tyrion is necessarily even right in his convictions. The show is a bit poorly plotted, but in the books Tyrion is mainly driven by revenge at this point. Him going to find Dany is more about joining up with an ally powerful enough to take out Cersei than about doing what's right for Westeros.
Dany is a classical conquerer in a lot of ways. She invades a country she's never lived in with an army of war-mongering rapists for the sake of power. The way she talks and acts ticks a lot of boxes about historical usurpers. The only thing that really separates her from a foreign tyrant is an expired birthright, and we learned long ago that birthrights and claims are meaningless in Westeros. The iron throne gets taken by power, and then the descendants of the new ruling family are considered to have a claim to the throne until they too are cast aside. The Targaryens took the iron throne by force, Robert took it from them, Cersei took it (twice) with her plotting and scheming. Dany has no valid claim and no business being in Westeros beyond the obvious revenge motif. Her father was rightfully cast down during Robert's Rebellion.
You can have her take the iron throne, but you can't do it while pretending that she's anything else than another highborn who thinks it's her right to rule over others. Personally I think having Dany realise that her reasons aren't purer than anyone else's would make for a far more interesting conversation than the self-mythologising white saviour narrative they've been building. A satisfying conclusion to the story in aSoIaF would be the beginning of the end of the feudal era and people like Daenerys, and I do think Martin's writing is heading in that direction. As far as the show is concerned it's completely up in the air at this point though, but one can still hope that they reach some form of closure instead of just ending the narrative after the last battle has played out.
