Need Suggestion for Background Check

Hi monkeys, I am an incoming SA at one of the BBs this summer. I got some issue with the BG check and hope to have some advice.
Here is my situation, I interned TWICE in one team but the team is jointly formed by two companies. I choose to have internship certificates from each of the company. In the screening process, the person I listed as my supervisor at Company A mistakenly said he supervised my internship at Company B because he indeed works at both companies. When the BG check agent raised the question why he said the wrong company he explained how the “two companies work together and he doesn’t know how I later dealt with the internship certificate things because he is only responsible for supervising my internship job”. Later the agent said he will find more about the companies through internet.
I want to ask, how serious this kind of mistake is? And if the BG check agent flag it as a problem, will the HR get back to me and do I have chance to explain?
Thank you guys!