It does not really make a difference. In practice, I can imagine that border guards outside of France might be less familiar with French documents and are a bit more likely to let your friend slip through but Schengen consulates often have lists of all the documents that count as an official invitation (as an example, here is the list from the Belgian embassy in Kinshasa, DR Congo). I don't know for a fact that each and every border crossing point has such a list at hand but in principle the rules are exactly the same and there is no guarantee that they cannot check either.
Note that such invitations are especially relevant for people who need a visa (and in that case you really need the right one because you have to apply to the French consulate and they will check). Third-country nationals who do not need a visa might use the attestation d'accueil to establish the purpose of their trip and explain why they don't have acccommodation but border guards do not always bother to ask for it.