>> minimum time between sync interval is 30 mins
This is for event based sync -- e.g. your device connecting to WiFi, mobile, there are other events too. This is for users who don't want to use scheduled mail sync, but need to get new mail when they get home.. that sort of thing.
The "minimum interval" helps avoid the app constantly checking mail if the device connects, then loses connectivity, then connects again, ....
It has no effect on scheduled mail checks or push mail. If you don't use event based mail checking, just ignore it.