This isn't true. Most MVHRs have a summer bypass mode in which they admit the exterior air without retaining any interior heat, but they do not cool the air entering the house.
The system in my apartment specifically calls out cooling recovery, but maybe that's not standard
Do you happen to know what make and model? The only cooling functions I have found besides summer bypass involve a separate cooling loop that ultimately relies on a heat pump. I'd be interested to read about an MVHR with this facility.