Who told you that you were required to hire a guide/what exactly happened?
This has come up enough that I think they do this just to get extra money out of American tourists. When I was there last March, I was with a tour group, and they wouldn't let us into the park without a guide (even though no one from our group was going to climb, me and my friend stayed and did but that was entirely separate from the school group), so we just paid someone $40 to get in the bus and ride with us to Tambopaxi. Then he left and there was no problem after that.
As long as your not solo, I would say that this time of year, there's probably enough people on the mountain (Cotopaxi), that no one would take notice or care about whether or not you had a guide.