If you go over to the battle.net eula: http://eu.blizzard.com/en-gb/company/legal/eula.html
There's this section:
Consent to Monitor.
WHEN RUNNING, A GAME MAY MONITOR YOUR COMPUTER'S RANDOM ACCESS MEMORY (RAM) FOR UNAUTHORIZED THIRD PARTY PROGRAMS RUNNING CONCURRENTLY WITH THE GAME. AN "UNAUTHORIZED THIRD PARTY PROGRAM" AS USED HEREIN SHALL BE DEFINED AS ANY THIRD PARTY SOFTWARE PROHIBITED BY SECTION 1(C)(ii) ABOVE. IN THE EVENT THAT THE GAME DETECTS AN UNAUTHORIZED THIRD PARTY PROGRAM, (a) THE GAME MAY COMMUNICATE INFORMATION BACK TO BLIZZARD, INCLUDING WITHOUT LIMITATION YOUR ACCOUNT NAME, DETAILS ABOUT THE UNAUTHORIZED THIRD PARTY PROGRAM DETECTED, AND THE TIME AND DATE; AND/OR (B) BLIZZARD MAY EXERCISE ANY OR ALL OF ITS RIGHTS UNDER THIS AGREEMENT, WITH OR WITHOUT PRIOR NOTICE TO YOU.
Now, i remember that there was some case in Germany that had something to do with Blizzard losing the case but i'm pretty sure that only had to do with some dude selling gold on his website. On one of the major bot websites, they say that "Botting in Diablo 3 is not against any law, except in Germany." <- not sure what they are referring to exactly here but i'd guess that it's an outcome of some lawsuit. Couldn't find anything that say that they are not allowed to scan your memory. I think that even if they are technically not allowed to, they'd still do it and you'd have to bring it to court against them if you have a problem...