This sounds to me like the teenage version of MIL purchasing a grandchild's first Halloween costume or Christmas dress without checking with the child's parents. As the kid gets older, the purchases get costlier. My MIL did both of the things I mentioned, and was upset when her "gifts" went unused. Ther were many "but I just" conversations in those years.
Many years later, I think MIL and I have a reasonable relationship. There were about 5 years of her testing boundaries, and DH and I never giving an inch when she started "but I just"-ing. Now MIL would not purchase a big-ticket, large or 'main' gift for our girls without asking. In return, we've let her take the "super-grandma" spotlight a few times. Sometimes I regret that MIL and I had those prickly years, because there will always be some wariness between us, but it is jut the way it worked out.
The difference is, my MIL responded to our 'training'. Your MIL seemingly just took your boundaries as a challenge. Problem is, she was never going to win.
If this is just the last in a long series of oversteps as you describe, I'd take it as a signal than it was time to limit her access to my family. A few posters brought up the issue of a car, what is to prevent her from bankrolling his first apartment without your consent in a few years, or something equally huge? I am (I hope) exaggerating, but I have heard of it happening. Recently I've been asking myself, " what positive impact does this person have for my family?". If the answer is none or not much, I'd be cutting them out, especially as, in your case, she has shown no willingness to respect you.