Am I a man of integrity?
Your dog guards your house from robbers and other criminals. But if it barks at your friends and relatives, shouldn't you shush it? Is that being ungrateful to the dog? 

Rice is the staple diet of most asians. But are you ungrateful to rice if you refuse to eat spoilt rice? You eat rice when it is healthy to eat. In the same way, agree with scientific teachings when they are beneficial and true. Reject them when they are mere hypotheses based on wrong views.

Integrity is the quality of being honest. It is Anatta like everything else. But Anatta does not imply that one should not cultivate good qualities.