They can only influence users' expectations of required fees in proportion to their hashrate, which you specified was small.
Only if block sizes are limited. If they are unlimited even a tiny portion of the hashrate can continually clear the market at effectively no cost to themselves, thats the whole point of this post-- creating a cost for doing so.
The size of the portion must matter since an even tinier portion could still mine all the free txes at 3x difficulty, but that much less frequently.
This is a challenge for the distant future, if ever. It seems pretty likely the value of the currency at the next halving will be at least double its value at the last halving (which was only 12 USD), with 3 more doublings already provided for at today's price.