Commercial Malwarebytes isn't on-demand, it's an actual anti-exploit/rootkit solution. I assume the free version, which only has the on-demand features, comes with these components anyways? Might explain that behavior.
My reason to trust them is that they seem to be generally respected still, I've been using them for a long time and they've yet to start annoying me with dark patterns and upsells - of course that's not a super great indicator.
Malwarebytes installs a program with elevated privileges that starts on boot and always runs in the background, and regularly sends data home - despite that it is an ON DEMAND scanner.
I have written to the company to understand this virus-like behavior, and have gotten no response.
Do you have a reason to trust them?