All this is true, except (as I said) I prefer theatrical gaffer's tape as the fix-all solution. But keep in mind that the argument was that the LM should have been a carefully designed, carefully manufactured spacecraft. That parts of it appeared to be taped together, as one would expect from a low-cost, low-effort handyman's solution, seems suspicious to people who can see a pretty obvious parallel.
Yes, we use tape that's not like the tape you buy in hardware stores. And yes, we use thin films. All of these have proper engineering explanations. Tape is better than a piercing fastener when dealing with laid-up blankets, because such a fastener would concentrate any mechanical loads on the fastener points. That's more acceptable with more robust materials like sheet metal. But tape is actually the best solution for mounting films in that way. It spreads out the mechanical load.