FT background check - informal role

During college, I worked on a project with a contractor to an F500 for a couple months. The contractor had a signed agreement and project scope with the F500. I completed work used by F500's marketing department and I listed on my resume that I was a marketing consultant to the F500. However, I was never formally paid, employed or contracted/subcontracted to the F500.

The contractor can definitely pick up the phone and verify my experience. However, just concerned about two things:

1. Is it ok if I leave this off background check forms? The forms ask for employment history and formally this is not. If asked about it later will I be accused of intentionally concealing?

2. Would a firm conducting a background check think that my resume is misleading and rescind the offer? For claiming that I was a marketing consultant to F500 (true in a functional sense), while I was not ever formally contracted or employed. I did discuss the work in interviews but the exact nature of the role never came up.

I know asking HR is an option but I don't want to draw attention to if it's a non-issue.

Thanks in advance!