Background check on contestable Cover Letter statement?

Hey,

I am a little concerned regarding the background check, so I was wondering what you guys think about this:

In my cover letter I stated that I did two internships at the same BB in two different divisions and received a full time offer following each internship. However in fact, as the BB does not hire two years in advance and I still had two more years to study, I did not officially receive a full time offer contract after the first internship but rather an offer for another internship in the following summer. I turned down the internship offer (for which they had an official contract prepared) but in exchange got fast-tracked to the AC for a different division at the same BB for the following year, got the internship and actually received an official contract for a full time offer. I did not think about this statement in the sense, that for a background check they might not be able to prove this fact. At the end of the first internship my manager asked me what the procedure is, as he was aware that I have to more years to study. I only told him that an offer in this case usually results in another internship offer (dont asked me why I had to tell him this fact :-)...)

In my CV, I did not mention any offers at all. So, if they do a background check, could this lead in any way to trouble as I am not sure if the BB recorded an official full time offer after the first internship?