I kind of agree - the fact that therapists seem to feel the need to put "genuinely" in front of "care" (No. 3 did) suggests that either they normally do not genuinely care or they know clients are suspicious. Or even the genuinely is an act.

Sorry to depress anyone, and I'm sure some do really care, and those who do clearly demonstrate it. But most of the time it's a professional caring. A little more intense than your dentist caring that you don't get cavities, but still professional.