River Girl, I now happily have Genius Mixes removed on my iPhone, iPad and My Mac. Here is what I had to do:
Short Version - You have to turn off iTunes Match if you have it running on all your devices, then turn off Genius, Then you will still have Genius Mixes remaining on your iPad, iPhone or iPod Touch, so (and this is from Apple) you have to restore your iPad to factory and restore from your backup. (I actually did that on both my iPhone and iPad and it worked.)
Long Version -
1) I found out under Apple terms and conditions that iTunes Match now REQUIRES Genius. Here's what it says:
When you use iTunes Match, Genius will begin associating information about the media in your iTunes library with your Account;... You will not be able to disable Genius while using iTunes Match, so if you prefer that we do not collect and use information from your iTunes library in this manner, you should not use iTunes Match.
So you must turn off iTunes match if you have it running. Here are the steps to turn off iTunes match:
--- How to Disable iTunes Match ---
Step 1: Turn off iTunes Match on your computer
store > Turn off iTunes Match.
Step 2: Turn off iTunes Match on all your devices
iPad: settings > music > iTunes Match (off)
iPhone: settings > music > iTunes Match (off)
Step 3: Sign off of your iTunes account
store > sign out
Step 4: Disconnect your iPhone or iPad if they are connected. Then reconnect.
(Now you see the Sync Music dialog back and no longer see iCloud message)
2) Next with iTunes match turned off technically Genius can be turned off, but the Mixes remain on your iPad, iPhone or iPod Touch and you can't delete them, so to get rid of the Genius Mixes already on your iPad, iPhone or iPod Touch, you have to restore your iPad to it's original settings and then restore from your backup. (Make absolutely sure you have a recent backup before restoring).