There's no shortage of folklore about Jobs hand-picking teams, as I'm sure you know, and moving around at Apple is very social by its nature. You have to make a conscious effort to end up in a position where you get an opportunity to build Swift, or iPhone (I mean building it, not keeping it going; vast numbers of people keep it going now), or Apple Watch unless you're hired into an essential role for something like that. Most people at Apple are doing the same things you and I do: upgrading Cassandra, diagnosing some OS bug that only appears on certain phones and carriers, localizing a piece of iTunes. So it becomes a question of how much you're willing to invest to earn your place at Federighi's side on stage, launching your passion that will change the world. For some, that equation breaks the right way. For me, I need more immediate feedback. Make sense? More me than them.
My time in the peninsula taught me that I value small, scrappy teams more, and that I'm not cut out for Facebook, Google, Apple, and friends. For that very same reason, I'm not the best person to ask on whether you should work for Apple or Google: some people thrive very well in large-scale corporate organizations but it isn't for me. In general, I'd wager a new grad should do a peninsula tour before getting into the risk game up 101, but I think that's a very myopic view, if I'm honest.
So i'll always go with a smaller and effective team than being part of a very big company where my role is more or less insignificant.
My culture screen was in-person, while I was being interviewed technically. Part of their process was getting to know me. I'm relaxed in interviews, joke around, and have a good time because at the end of the day, we need to like what we do. I find that this confidence has opened a lot of doors for me, but I do have to work very hard to project it given my internal strife. I often find that interviewers are more nervous than me, frankly, because as an industry we tend to toss people in a room who are themselves suffering from imposter syndrome and ask them to gauge someone they've never met with very little interview training. I was interviewing for one company on my third day.
I am the polar opposite of what I would consider to be someone who "fits Apple culture," in general, but it's worth remembering that there are vastly different cultures in different areas. I'm fat, I don't dress well, I'm largely unkempt if left to my own devices, I'm not a social butterfly -- put a soldering iron in my hand and I'll have a good time. I enjoy theoreticals about encryption and side channel attacks. I identify more with Woz than Jobs. Universally, across the board, every time I told someone I'm an engineer at Apple I got the look up and down and "you are?" in reply. I think people have an image of Apple that's formed from the typical customer and perhaps the retail folks; while that's true to an extent (what's served at Caffe Macs is an often great example, but you can find a kick-ass burger if you know which one to go to), I didn't find that Apple struck me as especially hipster or faux-cool or however you want to think of it. Again, maybe my area, but typical Web startup people generally break that way, so I would have expected Apple to reflect it, but no. That's neither here nor there and represents a very compartmentalized view. (I didn't work on Infinite Loop, and when I made journeys over there I got a different feeling, so that might be related.)
Just based on my own experience, I think team fit goes way over culture fit, and I don't think OP's experience sounds like a culture screen.
The other difference is that my process was practically a mirrored copy of Google's, with recruiter courting, technical screen by the recruiter, deeper screen by the #2 on the team, in person interviews. I interviewed for two different teams at Apple (one no-hired me, which was fun because then I was responsible for some of their stuff), and the process was nearly identical, except the no-hire team put a pair of people in the room and my accepting team put only one for each interview. At no point was FaceTime ever used. In fact, I wasn't aware that was a norm anywhere, but I admit that my purview was limited to my area.