You were told that would happen i you close two at one time, or if you close two over the course a few years?

Most people don't close two at a time, so if that's what you considering doing, we may not have info on that.

I'm not aware of people being routinely denied Barclays cards just because they closed two of them at some separate points years apart in the past.

But to a bank, closing two cards years apart is very different than asking to close two cards at the very same time. (The latter may imply to the bank that you might be in financial trouble, and that would be hard for you to disprove.)