I don't know if this was the cause or not but:

The machine thames has two IP addresses.  One on eth0, the other on eth0:1.  
Once I added both addresses to the host file on _both_ machines, amrecover 
happily restored  the file.  I'll admit I have no idea why this should make a 
difference, tho.  All traffic I could see went thru the the primary eth0 
address.