Well, sort of. I was browsing the ridiculous paper instructions that came with my Logitech k400 (crazy, I know!) and discovered that for this model, holding down FN and then left clicking the trackpad turns off the tap to click. It is still early days, but rough measurements suggest that this makes the unit less annoying by 3 orders of magnitude. This isn't as good as a general Pi solution, but it suggests that for many keyboards, there is a way to fix the damn problem. Searching for solutions on the keyboard end seems like a good bet.
And no, I don't know what mental disorder you would need to have to make you think tap-to-click was a good feature to activate by default.