You do not say who owns the dry lake bed. That is: under what entity was the ranger?. Was he a state ranger? Fed. ranger? County ranger? city ranger (or park worker, etc...)? Because the answer varies. And even within state or fed, there can be various distinctions within their land. A weak example would be: state "parks" verses state road right-of-ways (like ..... if you wanted to detect along bike-paths that bordered state roads, for instance). So the site that Sandman linked you to might sound dire for CA, but may only refer to state park land (not other forms of state land, and other levels of govt. property down to city, and county levels, etc....).
And as you can see, regarding state parks, it basically says to inquire at each kiosk. The problem there is, you merely put yourself at the whim of whomever you happen to be talking to. Like one could say "no" one day, and another one can say "yes" on the very next day! A humorous things like this happened here in CA: A particular state park here in CA used to get detected routinely, and no one ever cared (yup, in full view of rangers, and no one ever cared!). One day though, a newbie md'r shows up at the kiosk and asks (perhaps taking the advice of the fmdac state's list?). The ranger who fields his question says "hmm, I don't know. I've never had anyone ask that before. Let me find out for you" He gets on the phone, makes several calls hither and yonder, consults various dry-dusty rule books for minutia, etc... He returns to the window and announces "no" and cites various cultural heritage indian stuff as his best rationale (never mind that indians here had no refined metals!) Later on, other long-time md'rs in that same locale, who had never been bothered before at this state park, all of the sudden started getting booted! You can see the psychology at work here: Apparently this same ranger, who now has this "pressing question" in mind, passes md'rs later, and now must be thinking "aha! there's one of them".
There was even one state archie that tried to say state beaches here were off-limits! (he was harassing a friend of mine). This seemed totally bogus, because state beaches here are ROUTINELY detected, and no one cares less. So a few of us got ready to enter into a legal jousting match with this busy-body. But the more we looked in to the minutia of the state owned beaches (afterall, they are a part of the state park's sytem here, are they not??) the more we realized that if enough stink were made, and you asked enough questions far enough up the chain of command, that there might, in fact, be various rules that could indeed trickle down to apply to something as innocuous as state beaches. So what did we all do? Left good enough alone and did nothing! (odds are, this fellow would not see any of us again, as it was just a fluke that he happened to be at that beach, on that particular day, d/t there was some sort of conference going on that day there). So sometimes you must read between the lines with these state rules websites. I mean sure: don't tromp on obvious historic monuments, of course.
If your dry lake bed was a state-of-CA operated park systems park, and if indeed it is a historical spot, and if in fact you do hunt for nuggetts and metrorites as you say, then I believe he is wrong. Just tell him you're looking for meteorites (as you yourself say you do) Because meteorites fall from space. They are not man-made, nor historic. So if you were to say you were hunting for meteorites (or the boyscout ring your dad lost there when he was a kid), then I think you'd be doing an allowable form.
As far as hunting military camps, once again, you are vague on the question. You do not say if it's an active military base (many WWII era training basis are still active bases, and got the yazoo security status after 9/11) or if it's abandoned -as in, not even fed. property anymore. There are actually decomissioned bases that have been turned over to BLM, or neighboring cities, and even portions sold off to private investors where housing tracts are now going in, etc... So to simply say "WWII training base" can leave a wide-array of current statuses!
But assuming you meant still active, yet open-base policy ... Or at least, still federally owned, although maybe in an abandoned state now, all I can tell you is, there is one that fits that description near me, and we hunt it all the time with no problems. Now is that to say that if I started asking enough people, "can I?" that I might not eventually find someone to tell me "no"? Of course not. But as it is, security just comes by, sees us, and just makes sure we're not entering in to the boarded up buildings themselves.
) they might question their process of owning everything in this country...
