|   Could it be the router?

I don't see how/why the router should behave differently depending
on whether there is a NetBSD box bridging or not...

There is no NAT.  (Even if there were, why would the presence of
a bridging NetBSD box make a difference?)

|   I haven't used bridge(4) [I don't not presently even have a machine with
| the man page]. Is it doing proxy-arp'ing for other IPs, or is this a layer-2 switch? 
|   I wonder if the router gets confused by two hosts with the same MAC?

There are no two hosts with the same ethernet address;
bridge(4) works by setting the interfaces into promiscuous mode.
Yes, negotiation with smart components could be an issue, however
I believe my assorted topologies ruled that out.

	Sean.