In the popular language, being considered "busy" is not complementary. The urban dictionary makes a hash out of this one, so here is my take on it:
You take great importance out of seemingly unimportant things to such an extent that it is annoying.
"Stop being so busy - I am going to drink my recovery shake in a minute"
In my athletes eyes, I surely am a busy bastard. 98% busy. The coaches of my team also may see me as busy. Even fellow sport scientists may be annoyed by my busyness from time to time.
As sport scientists, it is our job to be busy. Who else is going to do it? We have to demand more from our athletes than that are used to giving. Take urine cups on the road for announced & unannounced hydration tests. Restrict how many oil soaked bread sticks the players are munch down at Olive Garden. Ensure correct timing of subjective ratings following training or competition. Prompt fluid intake at every opportunity during matches. You get the picture.
Sometimes you do want to use your common sense: Demanding players static stretch for 15 minutes following training outside in freezing rain may be a little too busy when a large warm locker room is nearby. This will just piss your players off and you will be equally miserable.
The odd exception aside, you should stick to your guns. Remember that the right things don't become the wrong things just because a player or coach doesn't feel like doing it, and it certainly isn't our job to be best mates with our players. Beyond that brief pissed off scowl, you will be respected for it and your team will do better in the long run than if you had caved.
Stay strong, in more sense than one.