Clean Tapes Each Time You Back Up? What The Heck?

I was working as a student placement at a rather large company last year. One of our backup tape drives was acting up, and nothing I could do fixed it. So I phoned support. The first thing the guy asked, after half an hour of detail-taking, was:

Tech Support: "Do you use clean tapes in the drive every time?"

Customer: "No."

Tech Support: "Well, that'll be your problem. Use a new tape every time, and that'll fix it."

I was rather skeptical about this but decided to try it anyway. Of course, it didn't work. So I rang support again and got a different guy. Tech Support: "Do you use clean tapes in the drive every time?"

Customer: "Yes!"

(enthusiastically) Tech Support: "Oh, well, that'll be your problem then. Every new tape that's used clogs up the drive."