When my kids were little, my parents came to spend Christmas with us. When it came time to bring out the Santa gifts, my parents also brought out the gifts they brought, as well as the gifts my brother and sister-in-law sent. The extra gifts weren't specifically Santa gifts, but when they were combined with the Santa gifts, they filled our little family room. The girls were blown away when they came downstairs and found their floor covered with presents. They understood that some were from Santa, some from Grandma and Grandpa and some from Aunt and Uncle, but they still were awed by the sheer amount of presents. They had a great time opening up everything, and everyone had a great day.
Fast forward to the next year, when the out-of-town group wasn't expected until after Christmas. The girls knew in their brains that they were receiving only Santa presents, but their minds remembered the gift extravaganza from the year before. Even we, the parents, were a little dismayed at how tiny our gift spread looked without all the extras. I mean, they still enjoyed their Christmas, but when you're 4 years old and you can only remember the Christmas from last year, it's hard to keep it all in perspective.
I wonder if the OP could tell MIL that she doens't want her child to think that every Christmas is going to be a present explosion? If you want to keep things real at Christmas, it's probably good to start as you mean to go on.