I was kind of similar to this person. My dad worked at buffets and within the restaurant industry, but he always managed them - never cooked at them (does one actually ever cook at a buffet?). He prided himself on being the cook of the family but he only really excels at a couple of dishes. My mom's a decent enough cook, but just decent enough. Steaks were cooked well, and paired with ketchup.
So, I grew up picky as hell. I'm 34, and I can still remember my third date with my wife when we were both 21. I ordered a turkey pesto sandwich and said, "with no vegetables". My then-barely-GF blurted out, "NO VEGETABLES!?" without even thinking about it, which sorta shamed me but not in a way, obviously, that put me off from seeing her again, lol.
Turns out her dad loves to cook, and her entire family loves going out to eat. My restaurant experiences were, by and large, limited to Applebee's and other crappy chain restaurants up to that point in my life. So, I started giving things chances; I started branching out culturally while still trying to find meat-focused dishes within that cuisine. Eventually, we started eating at nicer restaurants.
Going back to what I said about steaks above, I made it to my mid-20's absolutely hating steak. I thought people were idiots for loving it so much. I went to a steakhouse (Kevin Rathbun Steak in ATL) for my SIL's birthday one year and avoided the steak because of those misgivings. I opted for the lamb, and chose "rare" when asked how I wanted it cooked because I figured I'd never had anything rare and I may as well try it. I immediately fell in love, and ended up trying a rare steak a few months later. Now, I'm all about that 30+-day dry-aged, incredibly well-marbled ribeye!
I also forced myself to stop picking everything off. Don't like something because of it's texture? Try a smaller piece of it and see if you like the taste and how that taste pairs with the rest of the dish. Slowly, things fell into place for me and I began to appreciate more. Then, we moved to the Bay Area and it's gigantic concentration of Michelin-level restaurants.
My first Michelin joint had a tasting menu, and I told myself that the food at Michelin restaurants is definitely going to be good. Whatever is on that plate is going to highlight what makes that ingredient so good, why people like it, etc.. So my mantra was, "just eat it". Don't normally like it? Don't care, because if I'm ever going to have it at it's best, now is the time to see what the fuss is all about.
Holy shit did my world change. At this point, I'll eat anything. Texture is where I still struggle just a bit, but I'm keenly aware of what I do and don't react to in certain ways. So these foods can't be the focus of a dish, but I'll never shy away from eating them if their purpose of the dish is more 'complimentary', for lack of a better word. Taking this approach has allowed me to teach myself to appreciate the flavor, which then prompts me to eat it again, which gets me used to the texture, and ultimately gets me towards not being bothered so much by it.
All that rambling is to say - YES, I completely understand where your friend is coming from and I have thoroughly enjoyed having a similar experience.