I still can't believe a scrum master is an actual FT job - last company I worked for had one FT scrum master for each project - so they ran the meetings and as far as I can tell, did nothing else - what the heck do they pretend to do for the rest of the week?
I went to all the same meetings, and was still supposed to actually develop software in between them all.
You say this as if it was a coincidence.
I'm allowed to say such things. Some of my best friends are scrum masters.