I had the Fitbit Alta (not HR) for a long time and wore it all the time, even for dipping and swimming (in the indoor pool). I never had a problem.

As mentioned, not too tight. But enough to wash them under running water (without soap) after sports. I've also left it on my arm while swimming in the river. I probably destroyed the guarantee, but not the watch.

As you can see from the description, the activity tracker should not be worn while showering or swimming.