Geez, that doesn't smell right to me. I have this funny faith in systems being deterministic, and that type of behavior doesn't come under that heading. Once a system starts acting "funny" I get all show me about proving that it hasn't been hacked, rather than waiting for something obvious (like your browser exploding in flames).
I would check all of your other users and verify that none of them have elevated privileges. I also suggest doing a full crawl of your own site (from an outside system), collect all of the hrefs and srcs, and see if any of the URLs don't look right. Also check your .htaccess file and see if it looks good. I had a customer's site hacked about 18 months ago and the primary damage was some extremely weird stuff in the rewrite rules plus some virus files being delivered as if they were images. We only discovered it when our Google Rank drop through the floor because of some 404s.
There have been some old reports of general methods to hack into WP sites. I mention it because you are running older stuff so it may be vulnerable to this (or something similar).