It is disturbing, to be sure; if they are being persecuted for religion. Even moreso if upheld in court.
Reading between the lines of the story (and thankfully, some of the lines themselves), it appears that the matter is not yet settled:
1) the county spokesperson appeared surprised to hear of the complaint and the couple has yet to try this in court. The county official may simply have been out of line. Or, the county official may simply have been doing their job in addressing a neighbor's complaint and misread the law... or read it correctly...
2) this may not be a religious issue, but a simple matter of shear numbers of people meeting regularly in a neighborhood setting. The Bible study is a regular event, and is attended by about 15 people. That does not sound like a lot, but the local law may simply read that regular events attended by some number of people (possibly less than 15) have to get a permit. I have heard of stranger laws on the books. And this one actually makes sense. For example, if the couple were holding a rave or a high stakes poker game every week and neighbors could neither sleep nor park due to the drunken revelry, I don't think we would have a problem with this same law.
3) though unlikely, it may be that the couple was persecuted but by an imposter. Someone exercising their own freedom of speech (though admittedly committing fraud and other crimes in the process) may have posed as the county official, and upon investigation this will be revealed.
I am the chief of cynics, but while this case is definitely one to watch closely, I'm not prepared to scream 1st Amendment just yet.
God is God... Get used to it.