Is it unusual to get an informal offer before any recommendation letters have arrived?
Hiring for a limited-term position like a postdoc is a much lighter decision than making a tenure-track offer.  Often, there is an urgency to the hiring as well, as many postdocs are tied to specific contracts with specific tasks that need to be executed on a fast time-frame.  As a result, "ordinary" postdoc hiring can sometimes run a lot more like corporate hiring than academic hiring: a fast process where it's more about the person's ability to fill defined responsibilities and less about their long-term potential as a researcher.  In a case like this, references are still important, but are more like a corporate hire, where they are confirming the candidate is what they appear to be, rather than causing them to be noticed in the first place.

It sounds like this is the case for your acquaintance.  That's great, if the position is one that they want.  Nothing is certain, however, until the offer is in hand: just as easily as an informal offer can be extended, so can it be retracted if the circumstances change.