As Joshskiizz said, it is more likely that you'd use mods since you've admitted to coming on the server with TMI.
Furthermore, It is -highly- unlikely that someone would be able to find a specific ore (in this case diamond) and then correctly guess the direction and height they need to mine that would lead them exactly to the next deposit of that ore (again diamond). I put down torches so it could be more easily shown in the screen caps:
(http://www.opticraft.net/proxy.php?request=http%3A%2F%2Fi.imgur.com%2Fx5Bo7.png&hash=3df0ad3b3f10cc65726ede3930afe00c)
The hole in the wall on the right was diamond.
(http://www.opticraft.net/proxy.php?request=http%3A%2F%2Fi.imgur.com%2F02IwN.png&hash=3fd8953da71c160a8ce355a32fa02496)
Then you "randomly" go straight (ignoring the redstone ore)...
(http://www.opticraft.net/proxy.php?request=http%3A%2F%2Fi.imgur.com%2FzvYNW.png&hash=5b7c020094875f22c34343edfbd5181f)
Until you turned right (for no apparent reason) and dug straight again then "randomly" up three levels to the exact location of some more diamond ore.
This is so unlikely to be anything but x-ray as to be laughable. Whether you used the x-ray mod or an x-ray texture pack.
Furthermore, you tried to avoid the ban by using the account "bull_terrier89", pretending to be a friend who was sticking up for you. I compared the IP addresses, and both accounts originated from the same place. Ban evasion in and of itself is an offence to be banned for.
In light of the evidence, ban evasion, and unwillingness to be honest once caught I'm denying your appeal at this time.