Update and clarification:
This was for the pool. I always ask for two towels per person and don’t think this is unreasonable. We aren’t excessive with our towel use and turn those in before we request more.
I understand Disney would rather limit to 1 per person than not have any available but that doesn’t excuse poor planning for a known peak crowd. Two of us went up to get towels and were only allowed to receive two towels in total for the four of us. I was told the other two people in our party needed to come get their own for us to get more towels.
In their defense, this was an only an issue on Sunday and hasn’t been a problem since. Hopefully, it was an isolated incident.