It depends on how you mean sensitive. Some people are very sensitive to others and are not callous, but others are indeed very sensitive and are often overly sensitive and they tend to be the most callous and crass people I come across as they take a slight or perceived attack or whatever, times what it really is ten-fold, and feel justified in behaving cruelly and callously to the 'offender' in a way far, far more severe and hurtful than what was ever actually done to them.
I would say I can be overly-sensitive, though I don't really fall into the callous behavior unless, ironically, one of those overly-sensitive people perceive me as malicious or try to hurt me when they thought I hurt them. I usually overlook it but eventually when this happens so much from one person where I figure out that they are sensitive but are reactionary, I play the hypocrite and deliberately hurt them back until they learn to get lost and leave me alone. But I have been hurt the most by these people. I hate them when I run across them, especially when I thought they were so nice, too. = /