I don't even buy that. They utilize way less land than roads do. Even a massive high speed rail is thinner than a small neighborhood road. The steel is likely the only really high ticket item.
You have to also think about what you are comparing. It is not fair to compare RRs designed for interstate freight traffic to local roads. If RRs were to be used for more local transportation, they would have scaled down by now to something that would not be recognizable as normal RRs. There would be much lighter weight rails than what is even considered light weight today. We would be using very small gauge rails to run through our neighborhoods. The cost of these would be significantly less than those of major RR lines today.
Oh, and it really doesn't help to use he word "public" in any of this conversation. Roads are just as public (or not) as rails/buses/trains. All are mostly funded by taxes. It is not a good differentiator when comparing transportation modes.