Okay well if your Mew says you received it from an Event on Jun. 26, 2008 it is most definitely hacked because there was no Mew event at all that year. Although if it says your Mew was transferred to a Generation 4 Game on the Jun. 26 2008 it has a rather high chance of being Legit.
This Mew is the only Event Mew that has ever had an OT Mystry. As you can see if you click on the link it has the same info as your Mew. It is inside a Poké Ball, was distributed at Level 10 and it's OT is Mystry. This doesn't say it isn't hacked as players often check these event Pokémon out in order to hack more of the same Pokémon with the same details as the original Event Pokémon.
Although if your Mew's Trainer ID is 06930, your OT is Mystry and it says you met Mew in a fateful encounter then it has a high chance of being Legit.
Hope I helped :)