Copy remote files on nfs without round-trip

It seems that cp files* subdir does the naive thing and reads all the data into memory and then writes it back. Is that true?

Yes.

Is there a special command that does the actual copying entirely on the server the disk is physically connected to?

No, unless you can login to the remote machine with ssh and do the copying there.

EDIT There is some work going on to add "server-side copy" to the NFS protocol version 4.2 (current is 4.1). See e.g. http://www.usenix.org/events/fast11/posters_files/Lentini.pdf . Note that then using this feature would require a) NFS clients and servers supporting it b) a new syscall for the client OS (maybe reflink or copyfile()?) c) support for using the new syscall in the usual utilities (cp, rsync, etc.). My guess it will be at least several years before anything this sees the light of day.