If it was obviously bogus (think SLAPP territory) then that would make sense, but I don't think it is as likely to get their attention if the offending behavior can reasonably be classified as a potential violation of the CFAA.
(Whether it is a violation or not, I certainly couldn't say, but my point being that there is a reasonable good faith interpretation of the behavior that would not raise eyebrows.)
Strategic Lawsuits Against Public Participation. In other words, "Sue somebody when they criticize you, hoping the legal expense will make them stop." This isn't exactly the same scenario, but would be similar (in the poster's hypothetical) in that it was a lawsuit meant to intimidate rather than to seek justice.
(Whether it is a violation or not, I certainly couldn't say, but my point being that there is a reasonable good faith interpretation of the behavior that would not raise eyebrows.)