"Spiders and other crawlies maybe, but flying bugs are the real issue."
Ditto that. But stay away from the two month window starting roughly mid-June or so and you're golden with a tarp in the PNW. It indeed is about perceptions and mental comfort. For a similar issue, my wife liked using my backpacking hammock quite well, except that she never felt secure; she had the sense that she was somehow more vulnerable to wild animals in a hammock than on the ground, never mind any sort of objective analysis or data.
If it's important to you to break through that, however, what works is if the person is willing to push through it --- i.e., sleep enough nights in a tarp and you find out in your gut (not just in your head) that nasty things won't be constantly crawling over you! :-) At the end of the day, the person with the concern has to be willing (or you have to be willing to really stress your relationship!).