Under the current hobby rules (14 CFR Part 101 subpart E), which requires notification to airport towers and operators within 5 miles, they don't get to approve or deny, but then can object if they feel that the proposed flight will endanger air traffic.
The Part 107 authorization process either goes through the LAANC system, which just approves based on altitude restrictions in controlled airspace around airports, or through the older FAA authorization application portal, phone requests are assessed based on location, altitude and other proposed constraints.