I must admit I thought PDF's had kind of replaced Fax's as a secure document transfer method. We sold a property in our home country from O/seas a few years back and that's how we did it. Lots of documents requiring signatures.
A PDF isn't a "document transfer method". It is a document file format. A transfer method would be e-mail, snail mail, commercial courier, text message, etc.
The PDF format is not a secure format. Even a flattened PDF can be fairly easily intercepted and changed by someone with minimal technological ability. PDF's were originally intended to be a least common denominator format for exchanging documents without regard for what computer or programs the receiver has. PDF's are designed to open-able, readable, and to look the way they were intended to. Adobe Acrobat does include a password/security feature for PDF's, but it isn't a universal feature and it thus hasn't caught on and become popular.
A fax transmission isn't particularly secure, but it's what certain entitles are comfortable with. There are nice, open source, easy to use, encrypted ways to transfer files via e-mail, and you would expect that would be what just about all institutions would be using by now, but many institutions (especially government institutions) are very slow to change.