Thickness only adds rigidity which dampens some of the vibration but not nearly enough to be the selling point. If it did, every case manufactured since will mimic the Zalman Fatal1ty FC-ZE1. The CM Elite 370 is almost at the bottom heap with the CM Elite 343 in terms of build quality, decent for its price.
The expensive workaround to this problem is to buy a new case like a HAF series or CM 690 series. The cheaper solution would be to get fan grommets
which isolates the vibration of the fan from the case. It definitely works unless you'd prefer a more secure mounting with screws which is also possible with this grommet