When you install certificates into the computer store and use auto-enrollment or manually request the certificate using the Certificates snap-in, the requesting computer account needs Read and Enroll permissions on the certificate template.
However, when you're using Certreq.exe to request certificates, even if they are computer certificates and use MachineKeySet = True, the requesting user needs Read and Enroll permissions on the certificate template. When you use Certreq.exe, the computer permissions are not used.