It's definitely true, and there are a lot of studies and papers on it that you can read that usually use the term "horse trading." It's an important thing for people to know about, especially extreme partisans who like to accuse people of "conspiracy theories" who are just ignorant of the way day to day politics works.

But a thing that's important to keep in mind is that most of it in regard to the US is an artifact of having two parties who stand for nothing in particular and are virtually (and sometimes explicitly) written into law; making other parties difficult or impossible to make viable at any level. In that situation, horse-trading between the two parties entirely determines the outcome of governance, and they can (and will) also work together on public messaging to create a narrative that favors both parties against their unsatisfied bases.

So this does not work as well in parliamentary democracies, where horse-trading between the two dominant parties (usually nominally representing workers and business) and their coordinated actions and messaging can result in the shrinking of both of them together, as we've seen all over Europe where the dominant "opposition" parties who have been trading off rule since after WWII have been shrinking to a third or less of the electorate and only holding onto government by explicitly cooperating to hold onto presidencies or by pressuring other smaller parties through the media to refuse to create coalitions with the parties that have been their biggest 3rd party threats in the recent past.

In the US, what happens is that the entire electorate shrinks, and the party who had fewer voters in that cycle discouraged enough to leave the political system altogether declares that they have a mandate to continue the same policies that their predecessor instituted.