Counterpoint: a welcome mat that says “welcome” or “come on in” can be used to circumvent such requirements.

I think it comes down to whether the limitation of entry comes from a restraint external or internal to the vampire. If there is some force that comes from people/houses that prevents the vampire from entering until consent is given, then I think you may be correct in that the permission goes as interpreted by the permission-giver. If it is a compulsion that comes from the vampire themself that they need to receive permission, then it comes down to the interpretation of permission as received by the vampire, and they would have more leeway to twist meanings to allow themselves entry.

Personally I lean toward the latter understanding as it is a simpler explanation of supernatural phenomena for such compulsions to come from the vampire’s psychology than explain some magical force acting on the vampire from the dwelling. It also makes vampires more sinister and therefore scary, which for a horror entity is good.