What happens is when a station applies, they sign saying their statements are truthful. The FCC presumes the licensee will be honest as they have the most to lose. A complaint is not ignored and must be verified. Generally speaking a complaint is filed by a person with nothing at stake. If the two were weighed together, the applicant would be given the benefit of the doubt, yet the complaint would be 'proven' and if it was, the FCC would act.
It appears this station is not on the air. A station must only adhere to a minimal schedule. Typically it is 36 hours a week. It's not terribly unusual for a LPFM to be on a couple of hours, off a few hours, then on for another show for a couple of hours as they hope to fill in the hours with more shows. The lack of anything on the tower, per the complaint, says something, however.
Sometimes there is some confusion. Sometimes the engineer that files everything is off in another state filling in the blanks the licensee tells them. For example, that engineer might ask the antenna and get an "I'm not sure". Then after some questioning might ask 'does X brand sound right' and the person says yes, they are positive that's it. One guy had received a CP for one spot but had the engineer research another spot a few hundred feet away finding it will work at that spot but didn't have the money to pay the engineer at that moment. In time it was forgotten they didn't file for a change and the distant engineer files for the original spot. Sure, that's irresponsible. They corrected it.
It is way too common for LPFMs to fudge on the facts just to get the license hoping nobody will take a close look.
The FCC jumps once they have you where they want you. However long it takes to nail you to the wall is how long it takes. It's kind of like the police. They don't bring you in until they have the evidence to charge you. A witness can say something but they verify the witness statement first.