At a company I worked for, a vendor provided text files available through HTTP with a url that actually ended in .txt
I think that in that situation I used something like this to download it, but it's been a few years. I think your ability to use something like that would depend on a lot of variables in how ShareFile has structured their hosted files of course.
What might be a lot easier, and most file hosting companies provide this - I just googled and it looks like ShareFile does - is accessing them via FTP, which can usually be accomplished using VBA (especially if it is FTP and not SFTP - but if it is SFTP, I recommend using PSFTP.EXE)
Yeah this is the reason FTP is the way to go. I use FTP on Adrive and several other file hosting services using VBA. They practically all offer it, so why use the web approach if it's harder.