Another problem reason a fighter unit wouldn't take a non-fighter guy...
Unless you get assigned a fighter or bomber, (or go through Sheppard) you have not flown the T-38 nor have flown any tactical formation, nor have operated with a 'single seat' mentality...to top it off, you did not complete IFF (Introduction to Fighter Fundamentals...LIFT for the old guys).
Guard/reserve units do send brand new 2lts through UPT...but he still has to do well enough to complete all the above mentioned training, + the training on the actual combat aircraft.
To be blunt, they wouldn't want to waste the money and time on a pilot who already demonstrated the limits of his abilities/motivation.
(BTW, this does not apply to FAIPs who didn't get a fighter...there is a possible very slim chance for them)
But you know what, if you work hard, and do your best, you will get a fantastic assignment and great career...maybe not the one you want, but one non-flyers would be jealous of.