I think the reason the quilt police say - NO SHEETS - is because they can be difficult when hand quilting. This is because of the higher thread count. Also, a treated sheet MIGHT shrink less than the cotton fabric off the bolt. I would prewash your other fabric to be sure it has gotten its shrink out!
Having said that, I've used sheets for backing a number of times and the quilts turned out fine.

I look for flannel sheets to use for backing and if not in great shape color wise..use for batting in small projects.
I also use material that I find that I may not really like...large florals or whatever to use for backing.
My quilting teacher has some of the prettiest backs to her quilt using scrap pieces and odd blocks...like getting two in one. I love that Idea. So I always after my first two try to be creative with my backs.

Our ancesters used whatever was avaible so you can too.To me thats what quilting is all about, I love going to estate sales and finding a box of scraps that the old farm wife had made aprons and blouses out of.

I agree! Everytime i get yet another quilt out of my scraps I feel I'm honoring my grandma. She saved fabric from scraps/clothing to make her quilts. They were beautiful!

Tough to needle if you're hand quilting. Great for machine quilting

The other question to ask is..How is the quilt going to be quilted??? I understand that hand quilting would be hard to do with high thread counts. If machine quilting, then you should be fine. K

Vintage sheets are super-popular right now! Moda even came out with a line called "Dream On" that is based on vintage sheet patterns.

I have a lot of sheets that I use in my quilting and have used solid white many times. The only problem I have had was one time the sheet fabric pilled. Now I make sure they are washed first.

Here is a blog about using vintage sheets: http://vintagesheets.blogspot.com/

Ditto

I am using a sheet for backing on a quilt right now that I'm machine quilting. It was an odd flat sheet with no match and the color was perfect for the quilt. I have been pleasantly surprised!

Mid 70's I had very little money and used three sheets. Two stitched by hand in quarter inch "tunnels" where a fat yarn was pulled into the back side to fill the tunnels. Made an eagle that way, each feather and all details done this way then quilted with a sheet backing. Won a blue ribbon. I learned that a very small needle slipped right through all three sheets without a problem. Went on to using batiks which cost an outrageous $4 a yard in 1974, and looked nothing like batiks today.