For those following this thread, this appears to be the net result (as of this date) -- AS I UNDERSTAND IT...
Some systems (like LotusLive video conferencing) record videos using codec AP@L2. This apparently has better compression than the new AP@L3 codec in use by AVS Video Editor.
So, if you load one of these files into the editor, and do nothing else, there's no way to save it out again without bloating the original file size by like 3x.
If I ever figure out a way to do simple trimming of such files without blowing them up, I'll try to remember to post it here.