Well, I wouldn't say it was wrong, as I think receive can be used in cases like this (I think we can talk about receiving treatment). However, I think an MRI scan is too passive a procedure to speak about receiving it. Similarly, we don't speak of receiving our photo taken. I would simply say "I had an MRI scan".
I agree. It would seem illogical to be able to give someone an MRI (see sound shift's post above), but not for the other person to receive it. However, "I had an MRI" does indeed seem to be the most common usage.
True, but one would have to knock off the word "taken" for it to make grammatical sense anyway, and then it would just mean to receive the photograph itself. To use "receive" in this context, one would probably have to define a scientific-sounding term that drew attention to the technology itself rather than the end result. For example: