The compatibility matrix is correct. vSphere Replication can work with different versions of vSphere/ESXi, however, it is tied to a major version of vCenter (eg. as the link you posted shows, vCenter 5.5 U3 works with VR 5.5.1 or 5.8.1, vCenter 6.0 U2 works with VR 6.0, 6.1 or 6.1.1).
From the VR FAQ located here: Storage and Availability Technical Documents
Can I use vSphere Replication to replicate a VM between vCenters running different versions of vSphere Replication (eg. VR 5.5 to 6.0)?
To replicate between vCenters, vSphere Replication requires the same major version (eg. 5.5.x > 5.5.x) of vCenter and vSphere Replication at both source and target. This is the only officially tested and supported configuration. Check the VMware Product Interoperability Matrix if you have any questions about matching vCenter and vSphere Replication versions.
I understand about the major versions of vCenter needing to be the same in the source and destination sites to support VR. What I wasn't quite clear on was if VR had a dependency on vCenter or if there was another way to get replication running using ESXi hosts directly, or even if that was supported.
It sounds like if we want to use VR for any kind of migration work we will need to match the major versions of vCenter in source and target. Is that correct?
Yes, VR is dependent on vCenter and cannot be used without it. Regardless of the use case the vCenter major versions at source and target need to match. For specifics see the interop matrix.
Great, thank you for clearing that up for me!