Depending on the version of the OS and the version of Access being used the mde file may not run properly. If they have a 64-bit version of access, and the mde was compiled in a 32-bit version, it may not be recognized correctly, but a accdb file would work fine, and you could lock it out as well.
Also, if your using an accdb back end, and need to use a compiled front-end, switch to using accde front-ends instead, as those are the modern compiled versions and mde should only be used in versions of Access prior to 2007.
My only question for you is to find out if the users are running from a network location or a local folder - as running any Access DB front-end from a network location can cause issues. Have the accde file (or the front end) copied to their desktop first, then run from there.
Also, after download, you can run a file size verification to confirm the whole file was downloaded, as I have seen wifi connections lose part of the file during download, and then that causes corruption too. If possible, split the interface into multiple, smaller files, to make the download more reliable.