Could be that, The Engine Management Light could be a lot of things.
I'd film the air filter being removed and cleaned and if it is dirty, challenge them, however AC have a poor reputation (I hate them just for that awful yellow sticker on seemingly every car in Scotland) and they will probably ignore it because its a while since your service was done.
If I were you, I'd find somewhere else to get it serviced, although that's easier said than done.
If AC is the only place that you can practically take it, do some basic checks, oil, tyre pressures, filter condition, anything you can do easily and film them too. Recheck and film immediately after the next service.
Some people mark service items to see if they've been disturbed or changed, its worth marking the oil filter (photograph it) to see if its been changed (if you can get to it)
Its a sad state of affairs that we feel they can't be trusted, but the best thing it to protect yourself.
Some dealers have started to film removal and replacement of key parts and key service checks, its a shame they don't all do it