questions about FT background check after not getting return offer from internship

I didn't get a return offer from an internship. I didn't get fired and all of my reviews came back with meets expectations / exceeds sometimes. I think other interns were better and I may have not done as well in some of the social aspects. 

I recently got a FT offer, and I'm concerned that I may be marked as "ineligible for rehire" for that internship place. Are my concerns valid? No one asked me if I got a return offer during the interview process.