Any business that uses SaaS or externally-hosted software agrees to this. The question is whether your vendor has a reasonable access policy for that data, and what "reasonable" means hinges a lot on your vertical and the kind of data you're storing. PCI is a completely different ballgame than button clicks for example.
Increasingly, plenty of non-SaaS products work this way (e.g. Tesla cars, OnStar, your iPhone, apps in the Windows Store, etc.) Again the question isn't so much about "whether" to collect usage and bug reporting data, it's about getting the defaults right and educating concerned users to tweak them to a level where they are more comfortable.
> also tells them that you think they're so stupid that they don't know the difference between a bug and a user error
This is literally the case that OP came to us to solve
Having all their business data logged doesn't sound like a condition that any reasonable customer should agree to. In some cases, such as healthcare related data covered under HIPAA, it would be outright illegal. Asking for this kind of arrangement tells your customer that you don't understand the importance of confidentiality and security, and also tells them that you think they're so stupid that they don't know the difference between a bug and a user error. If a contractor suggested this condition to me, I'd show them the door immediately.
You'd also be taking on a serious risk. Even if it was legal for you to have the data, it could open you to legal liability if through some error of yours the data was compromised, costing the client money. And if you had possession of the data, you might get blamed even if the data leak wasn't your fault.
Even if you logged the data on the customer's own machines, bad things might still happen, like a bug in your logging code logging confidential data in plain text when it was supposed to be encrypted. It could then fall into the hands of an employee who wasn't authorized to see it.