The Mystry Mew was a real event Mew that was distributed in 2006 via trading with save files that were packed with these Mews (14x12, plus extra six onto the party, equalling to a total of 426 Mews).
I just so happened to get ahold of one of these save files, and after some examination and experimentation. I have come to the conclusion that the Mew you have on your save file in indeed illegal. Let me explain.
long explanation incoming: if you want the answer, the answer is that yes, the Mew is hacked
How a shiny is determined in Gen 3 and 4 has to do with the OT's TID (06930), the OT's SID (00000) and the Pokemon's personality value. The game does an internal equation and if the answer is less than 8, the Pokemon will be shiny. We can therefore use this in order to find the PID that makes the Mew shiny without altering the original SID and TID.
But before this, there are different types of PID methods. The one that is relevant to the Mystry Mew is the Reverse Method 1. We can use this to scale down the number of possible PIDs that would match.
So, If we run these conditions through a program that finds Pokemon's IVs and PIDs using the correct methods, we get a handful of results.
Firstly, the IVs, Nature and the PID of a legitimate Mew are as follows:
Docile, 30 HP/22 Attack/19 Defense/23 Sp. Atk./30 Sp. Def./29 Speed and 81EA4694
If we run these through a program, it is acknowledged as a RM1, the method we want. However for this specific Mew to be shiny, it needs the SID to be 56424, which we cannot have else it would be marked as illegal.
So now we know how the game decides if a Pokemon is legal or not. So let's try and find the PIDs that make this Mew become shiny using RM1 while retaining its IDs. After running through these conditions, we have loads of possible PID and IV combinations.
It is also acknowledged by the first program.
So let's try and punch this information into a save editor to try and make this Mew a shiny Mew. Except it is marked as illegal.
Turns out that this event Mew is illegal. I have tried the other values to no avail. There seems to be an aditional PID check to see if it is illegal or not, and 'shiny mismatch' confirms that this Mew is shinylocked and therefore a shiny Mystry Mew is not possible without hacking (or save editing)
