Now that's incorrect. Most recruiters normally don't tell whether there are more slots available, especially in the early part of the cycle, because either they don't know (some of them really have no clue), or just don't want to turn good applicants away for possible openings if some of accepted applicants turn down the scholarship in that particular branch. Many of my classmates were told by several Army and Navy recruiters that all 4 yr and 3 yr are too late to apply in the middle of their application process in December (they were all about to take their physical). Now those are the honest/well-informed recruiters, because the likelihood of additional openings in the future, given the current economy and all, is very slim (i.e. applicants would stay for the scholarship and job, and military would not expand the pool for various funding issues). Last year my AF recruiter dragged my application process for months until January (that's when it was finally submitted), and later told me in March that the selection was finished in December. Now, that's some dishonest OR poorly informed recruiter.
In any event, as far as the selection stat is concerned, it'd be best to ask SEVERAL recruiters in order to find out what's really going on. I did that, and I found out that many of recruiter's information seldom agree, except some obvious ones.
Obvious: Would HPSP cover my tuition?
Not so obvious: When does the obligation-payoff start? (Here, the answer is not after you graduate. Time starts ticking after you got your license, which would be as late as 5-6 months after you got your diploma. Additionally, if you elect to receive the 10K annual specialty bonus, which you'd be eligible while you have your license, it would incur additional 1 yr service obligation which would run concurrently with the HPSP obligation. So if you're not careful, the actual obligation would be not 4 years (if you received 4 yr HPSP), but 4 plus some time.)