As far as I know, every state has an age cutoff where this is true, but it's usually around 14. So sex with a 14 year old, and you're guilty, even if she had the hypothetical fake ID. Sex with a 16 year old, however, you have a plausible defense if she told you she was 18, and a reasonable person would believe her given the circumstances.
Actually, when I had checked about USA, the information I found said that the age of consent (cut off age, said otherwise) is variable between states, but also, that most states do not really have statutory rape as I meant it, it only based on the age of consent (as indicated by Viressa), not on the age difference.
The concept of "statutory rape" used in general outside USA, at least in Europe, is not the one described in Viressa's reply.
It is not about the age of consent (below age of consent, there is no valid consent anyway, that is why is called "age of consent"), it is about age difference.
E.g. even if she has the age of consent, if she is not old enough to have legal independence (typically, means if she is less than 18), if she was doing it with someone older, it was considered anyway statutory rape - in other words, even if she was old enough (mostly was about girls, but applies also to boys) to give consent, the fact the partner was above 18 meant that the consent was considered void and null.
Though last I checked due to some question by someone, I discovered even most, if not all, countries in Europe have eliminated that (one country I know of, eliminated that around 2010), so, now would only be a matter of age of consent, which in most countries in Europe is around 14.
From what I saw in USA, some have a form of statutory rape based on age difference and age of consent, and allow people to have sex with a partner even below age 18 or 21, if the partner is less than x years older (I think the maximum difference can be up to two, but in some case, only one year).
In others, they have the same, but if you are married she can be well below age of consent and legal age and yet it is OK (I remember that well, because the accepted age indicated in that "married although under legal age and age of consent" was as young as 13yo).
In one state, California, even if both are under 18, the fact they did it when they were below 18 means they committed a fellony, though if I remember well is marked as a minor thing.
One State says the age of consent (16, if I remember well) is sufficient even if the partner is a full adult, but not if the full adult has a role as supervisor (e.g. teacher), legal tutor/administrator, etc. - but that limitation disappear the moment the younger partner reaches 18.
That is why I said the rules in USA are far from being simple, at least for the younger people - in one state they may be an happy very young couple, the moment they cross a state border, even being still in the country, they can be arrested