Banned from Walmart for My Friend's Crimes

My question involves criminal law for the state of: New York
So I was in walmart tonight with my two friends, K & D. Through the hour we were in the store my friend, K, drank half a can of soda (which he didn't pay for), put a hole in a roll of bubble wrap and took a worm out of a can of bait and threw it at my other friend, D. My friend D was tired so he left us to sit on a chair during most of our time at the store. As we were leaving the store, my friend K got brought into the managers office and they told me to come too because I was with him.
They planned on charging him with vandalism but the state troopers (they had called) said none of the charges they were planning on giving my friend actually fit the crime. They ended up just giving him a ban from every walmart in America for the rest of his life for trespassing and he agreed to pay for the few things he damaged because he felt bad.
My problem is they charged me with trespassing as well because I was with my friend K, instead of sitting around with my other friend, D. I am now no longer allowed in any US walmart for life when I didn't steal or damage anything.
They scanned my ID and pressured me into signing the trespassing form.

I know what he did was foolish but are they allowed to charge me?
Is there any way I can get this ban removed or reduced?
What should I do?

Wal*Mart is free to ban you. They don't need proof that you did anything. If you enter a Walmart again and they catch you, you can be charged and convicted of trespassing. You can try appealing (in writing, do not go to the store) to the local manager and perhaps the corporate offices. But until then, may I suggest you be on your best behavior and keep away from your criminally inclined friends while shopping at Target.

When writing the store to remove the ban, it is best to write the Corporate Office, address it to Loss Prevention Department.

Until you get a letter stating you are free to shop, do not enter any WalMart, period.