That's just one piece to "fair use". In determining whether the use made of a work in any particular case is a fair use the factors to be considered shall include:
* the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;
* the nature of the copyrighted work;
* the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and
* the effect of the use upon the potential market for or value of the copyrighted work.
It doesn't have to pass all those tests but it likely will need to pass more than just one of them.
Fair Use is an affirmative defense. That is: it's not a right to use copyrighted works, but, in the event infringement is alleged, it may be invoked as a defense.
Specifically the language of US statute is "the factors to be considered shall include". Which can be read as also allowing other considerations. Though I don't know offhand of specific legal gloss or caselaw demonstrating otherwise. The Wikipedia article you cite has that specific claim flagged as "citation required" at this time.
* the purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes;
* the nature of the copyrighted work;
* the amount and substantiality of the portion used in relation to the copyrighted work as a whole; and
* the effect of the use upon the potential market for or value of the copyrighted work.
It doesn't have to pass all those tests but it likely will need to pass more than just one of them.
http://en.wikipedia.org/wiki/Fair_use