But it's even messier than that. If we accept the boys as legitimate heirs then the phrase "princes in the tower" is inaccurate; it should be "king and prince in the tower". And if we do not accept them as legitimate then "princes in the tower" is even more inaccurate; it should be "bastards in the tower". (And to be really picky, there is only a limited space of time that they were known to actually be in the tower anyway.)
If we accept that Richard III originally had no designs on the throne, then up until the proclamation (on 25 or 26 June - Wikipedia seems to have both dates), the lords must have believed they had a king in the tower. (It's oh so convenient to have the royal residence and royal prison in one building ... maybe we should try that with our modern day arrangements.
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It seems to me that it doesn't matter which way you cut it, "princes in the tower" is an unsatisfactory description of the situation.