There is no more certain death knell for actual productivity than the need to look busy.
The reality is that a lot of projects simply don’t need a hand on the tiller at all times. They need high-level direction, but too much interference at the mico level actually hinders progress. It’s like baking cookies. If you want good cookies, you need to have a good recipe and you need to mix those ingredients well – high-level stuff. But once they’re in the oven, if you open up that oven door every five minutes to check on their progress and manually adjust the shape of the dough, you’re just… you’re just not going to get good cookies, and what you do get is going to take a long time and probably burn you once or twice.
So if you’re a baker, and your boss is really concerned with how busy you look instead of how well the cookies turn out, then the cookies are going to be worse.
All this is to say, if you find yourself in such a situation, you should do your best to get out of it. At least, if you want to actually get anything done.