The theory is not based on interest rates, but rather tax loss harvesting. People have a better idea of what their tax liability might be at the end of the year, and it’s possible they might want to reduce their Capital Gains tax bill by selling positions that are negative to lock in a loss, offsetting some other gain. That means more selling in December, so it would make sense to buy as close to Jan 1 as possible, when the extra selling stops.
But it’s just another way to time the market, and timing the market is a bad strategy for the average investor. Just keep investing on your set schedule, and you will find that you still do OK, with much less drama.