According to the C70 specs, it has GPU clearance of 320mm, so your GPU should fit just fine.
C70 specs: https://www.corsair.com/eu/en/Categories/Products/Cases/VENGEANCE%C2%AE-C70-Mid-Tower-Gaming-Case-%E2%80%94-Military-Green/p/CC-9011018-WW
Would you have any idea why (or anyway I could find out) why the EVGA CLC says it's not compatible?