Interesting. I didn't think search would find anything on this; it seemed like a kind of weird problem. Most of my problems are common ones - you know, the ones that never happen anywhere else.
Other weird thing about this - I can delete other AVI files, just not this one; also, I get the same error whether at the computer, or accessing the system over the network.
That, and I don't have the preview thing enabled; don't think so anyway - Explorer is set to look like Win98. Just tried the command line over the network and at the PC; didn't get it; hang on, going to try a few other things.
Just did MindStorm's idea of creating the small text file, and then doing erase *.*; that got it. Strange.