I think they can do what they want, but they can be ridiculed for it.
Flag code says you only lower the flag to half-staff for deaths of people when ordered by executive figures. What they did is disrespectful to the flag. It is one thing for a private citizen to do this, it's another for a governmental entity. What they suggest is inappropriate.
But, it's mostly just funny that they're so butthurt that they wanted to lower the flag.