A lot of websites miss the nonce aspect. This in turn creates an unfair environment and a major opportunity to rig events. Unless the user changes their client seed EVERY round this case is not fair. They will also have to in turn engage users to verify bets one by one to ensure their fairness. This isn't what anyone (Lets be realistic) does and leaves the vast majority of people open to being scammed. If an operator notices you are not changing your client seed EVERY bet they are able to change the outcome of rolls.
I think it's a bit too harsh to call it "fake" provably fair, as without a nonce it is still provably fair -- just perhaps suboptimal from a users point of view. But if you trust the client (e.g. you've audited a static version, or using some 3rd party client you trust) it's actually possibly better.
There have been a bunch of casinos though with "fake provably fair", the biggest offender I remember was the old 999dice which put a "betId" (instead of a nonce) in the preimage, which allowed them to 100% control the outcome. And then there's been dozens of sites with "fake" provably fair systems (pretty much 99% of all multiplayer gambling games that come out, they screw up the provably fair and it's not actually provably fair).
I would be trying to categorize sites (from best to worst):
* Trustless
* Provably fair (follows best practices)
* Provably fair (warning: suboptimal, not practical for human verification)
* Not Provably Fair (game design makes provably fair impractical)
* Not Provably Fair (for no good reason)
* Fake Provably Fair (claims to be provably fair, but isn't)