I'm as confident as you can be they do not click buttons.
I remember suggesting they will submit forms that indicate they are using the HTTP method GET but in doing so they can be sure it's unlikely to send data back and affect your DB.
Another way of looking at it is that even if they were to, it's unlikely to pass the internal linking value you'd be hoping for as it's unclear. It stands to reason that the recommendation is just simply we know not using buttons confers value and are not sure (but believe it doesn't) the button route.
Again, links in JSON and data-href styled attributes do get picked up quite frequently, so it may be that his experience here is from another behaviour elsewhere