The 40db figure is certainly bogus. There is a lot of bogus db figures going around this business. No non-ANR headset can possibly achieve 40db - except at several kHz or higher. 20db is much more likely. I collected some evidence for this practice years ago (from the manufacturers themselves) and wrote to some pilot shops; I think they just ignored it.
You can make a non-ANR headset work arbitrarily well by using a lot of pressure to create a good seal. ANR headsets deliver a given level of attenuation without needing the high earcup pressure, and the bose-x and the zulu deliver higher levels of attenuation than
any non-ANR headset, while using lower levels of pressure than most of them.
BTW an ANR headset doesn't inject anti-phase noise into the earcup, as such. They way it works is that there is a mike inside the earcup which senses the instantaneous acoustic pressure, and the earcup speaker is driven (by an amplifier) to null out this pressure. Due to the finite size of the chamber relative to the wavelengths involved, the nulling process works only over a limited frequency range (low frequencies) but the improvement is still vast.
Cheap ANR headsets, such as the crappy £80 ones sold for airliner passengers etc, often do a bad job and you get whistling/hissing. The aviation bose-x doesn't do that, but the £300 consumer version sure does (we bought one and sent it back right away).
"You can't polish a !!!!"
True, so if you are talking to RAF Benson and they are on their crappy mike, they will be hard to make out, but with a decent headset you have a better chance.
I fly a fair bit out of the UK and a lot of the ATC out there is only just hanging in there on their "ICAO Level 1 English"
Of all the junk in pilot shops (and 99% of it is junk), a top end headset (bose or zulu) is the one thing worth buying.