I suspect Justice Thomas has read and digested Rand but is justifiably reticent about saying so in public.
Justice Thomas is on record as "having strong libertarian leanings".
He's my favorite writer on the court by far. Reading through this opinion of his, it looks like something he's had on his mind to say in an official way for some time, and chose this particular case as an opportunity to educate both his fellow justices and the public in general on an aspect of modern jurisprudence that needs some light shined on it. I wish this had gotten more play. I suppose it's too reasoned a discussion to fit on a bumper sticker, which explains why it hasn't.
Alito's concurrence was pretty interesting as well. He pretty much came out and said in no uncertain terms that the law that set up Amtrack was unconstitutional on its face. Certainly, the fact that the head of the Amtrak board is not a sworn officer seemed to disturb him greatly. The right case on this would be really interesting.