Edit: Since people want to respond to this post instead of reading the entire thread, I also said the following about the plaque:
But it doesn't say the "Seventh Federation Starship," it says the "Seventh Starship." Obviously the sub-light ship wouldn't count as a starship, but the NX-01 would. Adding the word "Federation" would make the plaque accurate.
I'm also pretty sure (but not certain) that in the DS9 episode Trials and Tribble-ations one of the temporal investigation officers refers to 5 ships by the name Enterprise and is corrected to 6 (referring to the Enterprise E).
I've never believed that the NX class vessels are referred to as Federation ships.
Its pretty obvious that ENT was made after TNG and DS9(in real life folks), so obviously the statements made when those shows were written didnt include the NX. That is hardly the first contradiction in Trek.
The NX wasn't counted because it didn't exist during the times those shows were mentioning ships named Enterprise. The recent books however seem to have an offhanded comment about the NX-class once or twice since Enterprise went off the air.