I had a fabric store person tell me I wouldn't even need half of what I thought I needed but went ahead and got what I thought. Boy am I glad I listened to MY inner voice as I used pretty much all of it.
Maybe if you do again next year talk to the owner or manager of a fabric store and see if your class can get a discount there. Explain that this class teaches how to make a quilt and by getting your class interested in this craft they stand to benefit if any in the class wishes to continue quilting. You might also want to meet with all the parents before your class starts and explain to them the requirements for the class with a list to go home with. Let them know IF you will allow a sheet for the back if they want to save some money (if you don't want to allow it then don't mention) but all items on list are what you believe to be the min. amounts of what they will need and are not open for debate. If they wish to buy more to be on the safe side let them know that is ok but not less than what is listed. Give them an estimate of the price per yard but make sure to let them know it is an estimate and not the actual price. Maybe ask at the store for the price range so the parents have an idea.
As for this parent, I would tell her that the way you are having the class make their quilts requires the amount of fabric you listed and all students will be doing theirs the same way. If she wishes to make her own quilts with less she should feel free to make her own that way at home but this class won't and you would hate to see her child hurt if his/her quilt didn't turn out well if she/he didn't have enough. If she argues that the store clerk said the other amount should be enough tell her the store clerk doesn't know how you are having the class make this quilt. If that doesn't work maybe offer to let her teach it next year.
Good luck hope it all works out. Hope you can put pictures up here just make sure you ask the parents for permission if you do put their children's pictures up with their quilts.