Originally, the GCA of 1968 read to the effect that the local LEO had to approve your FFL application, not just be made aware of it to determine if any objections.
The wording was amended for passage, so we've been sending copies of applications ever since. The language was brought forward to the FFL 03 in 1986 when the new collector's license was originated.
So if an LEO doesn't want any FFL holders in his jurisdiction, it requires an affirmative act on his part to object for cause, as opposed to merely doing nothing and thereby failing to approve.