An acquaintance told me that in the early days of mass transit in the U.S., the big automakers of the day bought most of the passenger railways and shut them down to make the country more dependent upon automobiles. Is there any truth to this?

The wikipedia article on the subject

The version of the story that I've heard alleges that what GM bought and scrapped was specifically metro rail systems (especially eletric) within major cities like Los Angeles, usually with the conclusion that LA would actually have an electric rail system today if it weren't for GM's interference.

It is true that GM and other auto companies invested in transit companies that converted rail operations to bus operations, with the side effect that bus infrastructure is also car infrastructure. They did not shut them down, and apparently there's mixed evidence on whether the rail lines were originally profitable or whether shifting to bus operations would have been a wise financial decision even without GM's involvement.

There were Senate hearings and a trial, with several companies being convicted of being monopolies. As far as I can tell, the actual conviction was for being the monopolistic supplier of buses--which doesn't directly have anything to do with converting over rail lines.

So yes, there is some factual basis for the story. It's even possible that it's 100% true, but it's not known for certain.