Yes, I agree with you. English, in fact any language has its subtleties (nuances).
The use of care in a negative way is tricky indeed, hence people get puzzled by it. You are in good company.http://www.learnersdictionary.com/qa/I-COULDN-T-care-less-or-I-COULD-care-less
However, if you listen to native speakers, you will hear people saying “I could care less,” and you will know from the context and tone of voice that they mean they are not at all interested or concerned
As you see, it´s curious as sometimes they use "care" in the opposite sense!
Finally, there are also those senses of "not care" meaning - dislike be antagonistic toward something; hate:
Etc... So it is exactly what one does when a visit appears unannounced or otherwise at somebody´s office at his time scheduled to work!
So, the expression is still contemporary, kind of.