Much thanks for the prompt replies.
bradgrafelman, the problem occurs in Firefox, Chrome, and IE (I've only tested it on Windows thus far).
dagon, I know. I wasn't necessarily implying that they did anything to cause it; my thinking was more along the lines of, "Maybe my local Apache server is configured similarly to my host's; they're the experts, so maybe they know what's causing it in both places." Opening a support ticket was somewhat of a last resort, as I've looked high and low for an explanation. Given that two of the most seasoned people on this board (you and bradgrafelman) don't have an off-the-cuff solution, it seems not to be a widely-discussed issue. I can't be the only one; my setup is pretty "stock" in all respects.
Sure, I can give you access to some test material... buy an album on http://indietorrent.org (may I recommend http://indietorrent.org/alpharev ?) =). You could buy a song, but the file would probably be too small with which to test (unless you throttle your connection in some way). I could also throw another "test file" of sorts up on the site, such as a GNU/Linux ISO or similar. I can get to work on that if it sounds like a worthwhile option.
I should also mention that this happens no matter how the file is presented to the browser. In other words, this problem occurs whether I "pass the file from PHP to the browser via header()" or whether I provide a "direct HTTP link" to a static file that exists within the webserver's document root. Further, the problem happens on both of my hosted mediaTemple boxes; one is a (gs) (low-end POS, essentially) and one is a mid-range (dv) (CentOS 5.0 Final with Plesk 8.3).
Thanks again for your responses, guys. Looking forward to any additional thoughts you might have.