Mew has been shiny locked in all events except one. The Faraway Island Japanese distribution in Emerald. It was an error by Gamefreak and wasn't intended to be that way. People didn't know it could be shiny, actually they thought it couldn't. RNG wasn't around back then and there's no recorded case of someone actually soft reseting for it. Getting one by hacking the Faraway Island ticket is still a hacked mew. The possibilities of getting a legit, shiny mew and that it survived until the sixth generation are so, so, so, so slim, it is safe to assume all of them are hacks.
You can find more information on hacked pokémon in the
Hack/Scam Report Mega Thread's first post.
I get what you're saying, but regardless of whether Gamefreak made an error, it can still exist, can it not? If they were offering a 6IV shiny Mew, I could understand but just googling there are tons of examples of people soft resetting for a Shiny Mew, there's even YouTube videos (and yes, I understand that on a YouTube video there's no way to tell if it was hacked or not, or if its an emulator that's a straight rom dump of the cartridge or if the rom was hacked to be shiny, etc, etc) showing the capture of Shiny Mew, (
https://www.youtube.com/watch?v=rXB7a6k3bro ) so there are in fact records (lots of them) of people soft Resetting for a Shiny Mew, they're just all dismissed as being hacked. I myself got a shiny Jirachi from the Collosseum Bonus Disc and even though it cannot make it through Pokebank, it is still possible to get one (although that proves the Jirachi was an error on Gamefreak's part, if the shiny Mew can make it through doesn't that prove it was NOT an error on Gamefreak's part?). And if I could get a shiny Jirachi from the disc, why can't Mew be shiny too? I promise I'm going to drop the subject now, I just wanted to make the point that it was possible, just very unlikely. (after all, for a while you guys had the Wishmkr Jirachi with an ID number listed as 00001 - 10000 but no mention of the 20043 trainer ID number, which was the trainer number of North American Colosseum Jirachis at least (as that's the only number I could verify with my own eyes), even though you can find screen captures of Japanese Wishmkr Jirachi's with the 20043 ID number as well) but regardless, like I said, I just wanted to make the point. I will drop it from this point on, and I won't bring it up again, I promise.
Need a specific Berry? I have literally every kind. Need a Friend Safari HA pokemon? I have them all. Need a gen 1 - 3 (and a few from gen 4) Move Tutor Egg Move that can no longer be obtained? I might be able to help. Drop me a DM if you need anything and maybe I can help!
My first battle in a competition, January 2016: I call this "never give up!" :D YNUW-WWWW-WW3F-FMAQ