If we accept
- The only way between the top and bottom levels of Midgar is via train (assuming that staircases would be too heavily guarded for even Avalanche to try to take)
- Aeris would have to commute between lower / upper levels for work on this train
- The only way to ride the train is with a valid id card
- Aeris hasn't been arrested
Then ipso facto Aeris must have a "valid" ID card.
Why is this so hard to believe? There is no reason to suspect that she must have a valid ID card in her name or that the Turks even know what ID card she is using, so short of them sorting through every single commuter systematically there is no way to pin her down.
So, how did she get this ID card? Apart from the short dialog in the train, we know nothing about them. We do know they can be forged, and that Avalanche would rather forge enough cards for their entire crew than just steal some from drunk/asleep people on a train. Maybe this is because in their self-righteous nature they don't want other people to get in trouble for not having an ID card, or maybe ID cards aren't that hard to forge. Does this mean that Aeris could get a forged ID card? Probably. She is familiar enough with the characters in the slums (for example, that guy who are sick), and she is one tough cookie (I mean, she hangs out in a slum infested with HellHouses), so she is probably savvy enough to get her hands on a card. Hell, she's worldly enough not to bat an eye when it comes time to help get Cloud ready for Don Corneo.
But this doesn't mean she has a forged ID card. Let's look at this other scenario (spoilers ahoy! I'm going to try to not use anything other than FFVII as canon): Aeris is 7 when her mother breaks out of Shinra HQ with her, and knowing her death is near, passes her off to a woman who is waiting for her husband to get back from the Wutai War. Now, Shinra knows the Ancients under their control have escaped, and they would definitely be looking for them. But, Aeris and her mother were able to get to Sector 7 without being detected, which means that the ID card system probably didn't exist yet. So, some time in the next 15 years, Aeris (and maybe her adopted mother) probably went through the regular legal mumbo jumbo of getting an ID card. It doesn't really matter that she might not be able to prove her birthplace or lineage, as during Aeris's age of 7 and 16, the Wutai War was going on and creating refugees; she is also from the slums, so there is no reason that they would even bother with having some kind of accurate census to base that kind of information off of. So, one day, a bright-eyed kid walks into the equivalent of a DMV, lines up with a bunch of other slum trash and wants to get an ID card so she can ride the train up to the land of opportunity. The bored clerk (even if there was a clerk. It could just have been a machine) looks at her and says "Do you have the registration fee?", takes her cash, maybe a bribe, takes a photo and registers her under the name of Useless McGetsStabbedInTheBack.