That is extremely untrue and irresponsible of your manager. I got tested once just for peace of mind, because my other job is as a caregiver for a boy with special needs who is especially at risk of having severe reactions if he gets it. Then a few days after getting a negative result I developed hives which me being super anxious I looked up and saw there was a link between skin rashes including hives and asymptomatic Covid. That fortunately came back negative as well. I didn’t tell anyone about either test because I felt I might be just a little bit paranoid, but I definitely don’t think it’s taking away from people who need it, because we all technically need it since it’s being based asymptomatically.

Your manager should be appreciative that you’re taking the initiative to make sure you’re safe even with no symptoms. I have permanent respiratory issues due to smoking and my SM hears me wheezing and then asks me discreetly to take my temp again.