When passports were first introduced it was a bit chaotic and nobody really knew if they needed them for older ponies so many didn't bother. Some breed societies introduced them for registering foals and offered optional ones for older ponies, ditto re microchips, and I know plenty older ponies who were never planned to be rehomed never got them as they don't need them unless transported or sold..
I wouldn't be worried about whether the pony was genuinely owned by the person - if stolen she'd be more likely to want to sell her than give her away
so if you like the pony and she suits you and has no ongoing lami or other conditions (only having routine vet history suggests good health so you can check visually and make your mind up which you'd want to do anyway as shetlands aren't all the same despite appearances
)
If the Shetland breed society are extortionate to issue a passport go for the cheapest general purpose one, be it BHS, BDS, she could even be a sports horse
I understood you could get them for about £10 so it isn't that much for a free pony and she won't eat much
Just make sure she's a nice personality and you like her, and if so then that'd be good enough for me anyway..