It's not safety first if there's a but.
If they get a report of something obstructing the course of the track, yes they should inspect it every time it happens. The thinking that an inspection shouldn't be made because there weren't any obvious signs of injury is a fallacy. Part of the point of the inspection is to prevent injuries from happening. The line of thinking that something should not get checked out because nothing serious has happened yet is exactly how this situation came to be.
EDIT: Again, I will use Disney and Universal (and Cedar Fair parks) as examples of parks that are safety-first and would have shut down the ride immediately. I don't think the large amount of people in the park and waiting on rides stops those parks from taking the safety-first approach (to address the idea that no one would get to ride if the park responded to these complaints).
I have to disagree. Space Mountain and Soaring were closed last year for a month after California safety inspectors found deficiencies in the rides.