That doesn't appear to be the case with my setup: Drop needle onto stationary record, observe RTA display, and I see very little higher frequency activity. I experimented with hand-clap noises near the pickup head, even tapping on the thin aluminum platter directly and was surprised how little effect this had, and how effectively even the stock felt slip mat dampened these.
For my purposes, it seemed that airborne pickup of noise wasn't a big deal (at least not below lease-breaking SPLs), but if I wanted to be perfectionist about it, a record weight or clamp would suffice, and wouldn't have to bear down particularly hard on the record to be effective.
By far the biggest problem I observed was in the region 30 Hz and below, and so far as I can see, that's energy being generated by the building and it's occupants and passing right through the turntable's rubber feet to reach the pickup.