Confirmed and fixed in CVS. It is exactly what you suspected. I misused of the Apache table API. I assumed that the headers would be premerged (coming from the other Apache sever). This isn't always true, as you have seen.Yay! Time to CVS update!
On or around line 657 in mod_backhand.c, change AP_OVERLAP_TABLES_SET to AP_OVERLAP_TABLES_MERGE.
This will fix your problem. It will be rolled into the next release.
Thanks for the bug report!