I think most people would have essentially the same reaction to either FBI or state/local police showing up at their door with "[Police|FBI], open up!", and it depends more on whether they believe they've done something illegal than the reputation of the agency. This was my disagreement with GP(stavros).
Depending on how you expect the reader to answer all your questions, we could still be in full agreement, but my sense is that you're asking them rhetorically?
You can ask the same questions about a local law enforcement agency but the answers won't be the same for every one of them.
And then in terms of literal sentiment, most people aren't familiar with any given local law enforcement agency because there are so many of them, so they wouldn't know what to think, and some of them are quite bad. But the knowledge of the average person it isn't really the point.
Suppose you actually were familiar with the record of whatever specific agency just showed up. If you would still have to think "oh fuck" then they suck.
Depending on how you expect the reader to answer all your questions, we could still be in full agreement, but my sense is that you're asking them rhetorically?