Well put. After reading, I came here to say the same thing.

The times that I "Claude said:" are almost always a case where Claude gave the correct answer.

The real problem is if you paste "Claude said:" without reading what Claude said. Have seen this happen and goes something like:

Sr Engineer: "Claude said:"

Me: "But that doesn't make sense because of X"

Sr Engineer: (having actually engaged thinking effort: human) "Oh yeah, not sure why Claude said that, I think we should do Y instead"