this looks like Dryspace or the like. it is designed to go under decks and do exactly this. The stuff I have installed said it was not necessarily going to be 100% watertight.
It sounds like it needs to be addressed from the top, but under the deck boards. Perhaps just a few of the boards over the beam could be pulled (even with nails it should not be that big a deal) and some sort of fix applied.
Everyone is entitled to their own opinion, but not their own facts