Marketpress digital download files corrupt

So I have the problem with digital products in Marketpress where the downloaded files can't be opened (I can FTP the files from the server and open them no problem.). I've seen this same issue posted several times, and the resolution is usually to disable another plugin that's causing it, but at the moment Marketpress is the only plugin I have running.

The files are JPEGs about 200kB in size (I currently have Max upload file size set to 10000kB in the network settings). I tried zipping them but get the same problem (for zipped files it's exactly as described in this post https://premium.wpmudev.org/forums/topic/wpmudev-files-not-downloading-correctly).

I can get the downloads to work if I add
define('MP_LARGE_DOWNLOADS', true);
to wp-config.php (as mentioned by Aaron in this post https://premium.wpmudev.org/forums/topic/marketpress-downloadable-files-are-corrupt-after-download). That solution turns on redirecting instead of php serving, which I don't want to use for security reasons.

The only other thing I can think of is if a PHP or Apache module is causing it but then downloads work fine with the Easy Digital Downloads plugin that I'm trying out on another domain (same web host).

What else could be the problem?

I'm running Marketpress 2.8 and Wordpress 3.5.1 (as multisite).