> Even the U.S. Navy ships fire warning flares at other vessels when they approach close.
Yes. A helicopter is not a vessel. These kind of monitoring exercises are common amongst both Russians and Americans when operating near each other or their territorial waters.
Russians frequently overfly American and NATO craft. Russia has also been committing acts of sabotage around the world, but more specifically has been cutting undersea communication cables, so they are absolutely worthy of scrutiny.
The Russian Ambassador to Denmark stated that Russia would “thoroughly investigate all the circumstances of the incident”. That's not exactly a hardline statement indicating Russia knows it was in the right.