Are You sure????
For my knoledge, the 2 main difficulty are:
1) accuracy
2) drift
Think that the most famous factory as Agilent, Rhode&Schwarz, Gigatronic etc give no more than 3% accuracy.
I've seen the schematic of a hp438A and the most critical circuits and mechanics are needed to get both 1/f and thermoelectric voltage as low as possible.
But to answer to your question, A peak meter may read CW also.
basically it's a diode detector with a calibrate response law.
The response time depend on the "integration time costant" (R*C) that follow the detector.
As R*C increase, the meter tend to be a CW. As R*C decrease the meter tend to be noisy.