Saying that all Kindred are members and welcome to the Camarilla is true. It's a fact. It's a basic tenet of the sect. If you can follow the traditions, respect prestation, and generally, just not be stupid, you too can be a Camarilla member regardless of what clan/bloodline/political party affiliation you are.
That said, they won't make it easy.
In fact, it can sometimes be pretty hysterical sometimes if you stop and look at it.
As John J. Kaufman writes:
The goal of the camarilla is to get as many kindred as possible to follow their rules and *not* create situations in which mortals start a new Inquisition(1) or that lesser kindred rebel and try to attack elders(2).
It would be stupid of them to deny individuals the opportunity to join.
In cases where there are large groups of Kindred who basically follow the rules but don't want to kowtow (anarchs, indy clans), the elders are perfectly willing to let them exist as long as they have a way to assert some control when necessary.
Things get slightly more complicated when the group is one that has large ties to mortal communities and present themselves openly to their followers (Setites, Giovanni). The elders recognize that having that many clued in mortals is a recipe for disaster and aren't sure the Kindred can keep them from being a security risk. (re: 1)
As for the Assamites, those fuckers are dangerous. (re: 2)
The Camarilla doesn't kill, threaten, maim, abuse or beat anyone into joining, it pretty much assumes that if you're a kindred, you're a member, and if you want to be cute and call yourself independent, then that's fine, you'll join eventually when a Hunter finds you and you come running to them for help.
Now, Sabbat's a different thing because they're animals that have pretty much given up on the idea of trying to keep their humanity and their whole ethos is counter to the Camarilla's philosphy. Doesn't mean that the Camarilla exists to fight the Sabbat, just means the Sabbat makes the Camarilla's job harder.
Camarilla citizens learn all this during their accounting. They learn that it's the struggle against the beast, and that losing to the beast is breaking the masquerade and will lead to another inquisition against a mortal populace that is smarter, more techincally ept, and has better torches and pitchforks than the last time.