But since there is no independent organization that oversees "provably fair" I think provably fair itself is a bulshit.
Well there are 2 things to consider here.
1. ImplementationFirst of all, most sites use (slightly) different implementations. IMO the "nonce method" is pretty much the best way, generally if the site uses this (like most popular dice sites), you can assume it's okay (especially for a dice site where you can bet both hi/lo.) Obviously ideally you would still check if they are doing everything technically correct, but this takes some knowledge.
Some implementations do different things, and might be not so good. If you don't have the technical knowledge to check this, luckily there are other individuals that do frequently check sites. For example, Rollin actually didn't have a perfect implementation that potentially could allow them cheating and they adjusted/improved it quickly after I posted about it:
https://bitcointalksearch.org/topic/--687571 Another example, keepinquiet found out that PocketDice doesn't have a perfect implementation either that potentially could allow them cheating:
https://bitcointalksearch.org/topic/questionopinions-on-pocketdices-claim-of-provably-fair-1077905 Unfortunately they still didn't improved this AFAIK (so IMO best to not play there :X)
So there is no 1 organization checking it, but there are several individuals checking it (mostly dooglus, RHavar, keepinquiet and me I think - but everyone with some technical knowledge can do this.) I personally do plan to test all popular websites and compare all of the implementations in a proper/fair way (so not like those bullshit "review" sites.) But it takes some time to do this hehe.
2. Actually verifying your betsIf we assume the implementation is good. Still you have to verify your bet results to ensure you have not been cheated. It's good to learn the basics of how provably fair works here:
https://dicesites.com/provably-fair but even just using 1 of the verifiers on that page should be fine too. Provably fair is definitely not bullshit if you take a few minutes to verify your bet results.