ERG is just a pipe from the exhaust to the intake with a valve. Compressing and carefully releasing would be much more complicated and very much a not normal way of lowering exhaust temperature to reduce emissions.
Yes, on second thought, they probably confused secondary air injection ( https://en.wikipedia.org/wiki/Secondary_air_injection ) with EGR. It's very possible they were explaining secondary air, which doesn't compress exhaust gas, but does inject air into the exhaust gas to help burn more efficiently (not clear on the mechanism, I always thought it was a method to improve catalytic converter efficiency at startup).
I think the idea is that cold engines run rich, so injecting air into the exhaust gives the unburnt fuel a chance to combust in the exhaust pipe before getting to the catalyst. This is good for two reasons, first, it heats the catalyst up faster, which is good, and it also reduces the amount of unburned hydrocarbons.
I owned an RX-8 which had an air pump (secondary air injection) which would come on for about 30 seconds on a cold start. When the pump started going out, it would make a metal grinding sound. Drove like that for a few years until it quit working, and didn't think anything of it until SMOG time - $600 for an air pump which works for ~30 seconds...