Agreement in principle is basically solely based upon what you have told them. It can only really bite you in the bottom if your income is more complex than what you have said, ie if you are relying on bonus schemes if you are in sales etc, or the credit search throws up bad debt, or even debt which you have not yet disclosed. Student loans are one of them as they do count against your affordability.
Having spent far too long in the business (thankfully no more) I would always suggest getting a firm offer as soon as possible.
That being the case, it sounds like I do actually have one already (an offer pre-credit check). I assumed that an AIP was post credit check but pre- taking steps to grant it.