First, I don't think of an anechoic chamber as being designed for "sound isolation". Instead think of it as minimizing reflected sound (which I admit could be seen as isolating the sound source from the reflected sound). Semi-anechoic chambers are designed to replicate the ideal free field site. A fully anechoic chamber is the same except in all 6 directions.
Second, you can't say that the ambient sound level in any anechoic chamber must be below 20dB. The minimum level required depends on the minimum level you wish to measure and what you level of certainty you want/need. It may also be dependent on some industry spec. If you are trying to measure a jet engine at 140dB does it really matter if the background is 20 or 30dB?
So in regard to you question:
- Do you need to meet some industry spec?
- Depends on the minimum level you wish to measure and what level of certainty you want/need. (which also drives the measurement devices)
- budget (as always!)
ISZ