It's shared with other customers. I suspected cross contamination because I couldn't find a site at first that appeared to be actively infected; AND because I noticed some server issues around the time of these files being written. When I called them about the connection issues, they stated that they were having issues with the server. But, it's possible that one of my sites were actively infected. The part that made me think not was that the random files it appeared to want to load were not present anywhere in my hosting accounts.
The FileZilla issue (changing ascii files and playing havoc with my comparison utilities) was apparently caused during an update in which the setting for doing all transfers binary was switched to "auto". I always treated all files as binary. It makes for easier comparisons of text files.