It is possible that what the engineer referred to is that tuning with the capo in place is sliding the string under the capo pad, and thus wearing grooves in the capo, which then cannot hold the strings as well as when new. I know that this happens.

Another thought is that tuning with the capo in place preferentially tightens the string between the capo and bridge. Then, as playing goes on, the tension difference between capo-to-bridge and nut-to-capo evens out, letting the string go flat. I'm not saying this actually happens, but I can envision it happening.

Dave Oesterreich