Which I don't get at all. It's perfectly normal for Romance-language culture backgrounds, like Fieri's from, to pronounce an 'R' like a 'T' (or maybe a slightly softer 'D') in some situations. For example, a Spanish-speaking person saying "para ti" meaning "for you" will make it sound like pah-duh-TEE, almost like a slurred pronunciation of "pot of tea."
As a child, I grew up in the same house my mother did. Hers was the only non-italian family in the neighborhood, in fact, she could understand italian, because all of her friends were. I NEVER heard this particular language change. Rs were Rs, Ts were Ts.
I’ll add the caveat that I’m assuming that ‘Fieri’ is the real surname of his ancestors, rather than something he changed it to. Changing it *would* indeed be pretentious, though arguably no more so than the other million celebs that have a stage name.