Usually, no. There are hundreds of mystery shopping companies and they handle their shops and their scheduling differently. Some small companies use independent schedulers, like Kern Scheduling, exclusively. Some companies have schedulers who are direct employees of their company. Some companies use schedlers who work with their company as Independent Contractors. Some companies have their own schedulers and also use a scheduling company. Some companies have schedulers and also allow shoppers to self-assign shops directly on their Job Board, like Market Force. I've not noticed lower pay for shops that involve a scheduler.
The example you gave, scheduling shops with Kinesis, is interesting, because in my experience, the only way to schedule a Kinesis shop is through a KSS scheduler. Unless things are different in some other area of the country, all Kinesis shops are scheduled through KSS.
It would probably be worthwhile for you to sign up with more companies.