NX-OS Modify Distance for certain prefixes

It's well known that BGP backdoor isn't available on nx-os, but I can see a route-map set distance option to modify the distance for EBGP. Does anyone know if this works on received routes? I need to make the EIGRP path (if present) to be preferred.

If it does, it seems odd that there are many posts about this either suggesting alternatives or suggesting to modify the distance at the address-family level (e.g. here or here).

! N9k running 7.0.3i7x: nx-os-switch(config)# route-map RM-BGP-IN permit 200 nx-os-switch (config-route-map)# set ?   as-path             Prepend string for a BGP AS-path attribute   comm-list           Set BGP community list (for deletion)   community           Set BGP community attribute   dampening           Set BGP route flap dampening parameters   distance            Set the Administrative distance of route  [...]