Yes, I think the OP has misunderstood the phrase - it specifically refers to people who can't distinguish between differences in musical pitch. Being "tone deaf" means you can hear music, but you have not yet learned the skill to distinguish the pitch.

The colloquial phrase relates it to people who have not developed the skill to distinguish between emotional tones: it is used to describe an inappropriate social response in people who are not known to have a disability that impairs their ability to read social cues, particularly in the context of mundane callousness.

A manager who lays off half the staff because of "the recession" and then spends $10,000 on an elaborate lunch for managers would be called "tone deaf".