How do you know if something's peer reviewed?

Elsevier publishes a heck of a lot of journals. Some of them are excellent. Some are OK. Some are outright fraudulent: paid for by drug companies to promote their products. (they have been caught out on 6 of these, but who knows if there are others?) It is certainly not the case that the Elsevier imprint is evidence of quality.

I am not sure what you mean about access. Does Elsevier restrict access any more than other commercial journal publishers? (It is true that some of their prices are outrageous, but they are not alone in that either.)

It must be nice to be able to pick and choose where you get to publish.

Well, you can pick and choose where you submit, certainly. And while Elsevier has some extremely specialized journals, there are also plenty of other less-specialized journals that would be appropriate for any given paper (at least, in physics: I can’t speak to other fields). And on the access point, what I mean is that they make you jump through a lot more hoops to get them than most publishers. For, say, PhysRev, if your institution has a subscription, and you’re working from a computer with an IP address associated with your institution, you’d never even realize that it’s restricted access at all: You see a link to the paper, anywhere, you click on it, and you’re reading the paper. But for Elsevier, once you’ve found the paper you want, you have to go through your library’s site, prove who you are, find the journal and paper again, and prove who you are again, before you can read it.