That's right. A proctored exam is usually done by someone who is a local college or perhaps a local library. For example, when I did my undergraduate degree my proctor was my public library and it worked out fantastic! They had a reference center with a head person who I had all my proctored exams sent to. There was two people that were on the list for the "in case of questions be sure to contact". I never had any problems.
Grant it, depending on the professor the exam was either the mid-term or the final but in either case it worked out really well for me. Needless to say, a few months after receiving my IT degree I began work towards my MBA. At any rate, it's been one heck of a ride.
To answer your issue with exams however. If you feel a student must take something that I have experienced which I thought was totally awesome with my university is their multiple choice. I'm not sure how they did it but when I had gone through the final exams online they were REALLY hard. I'd study like crazy but the way the questions were worded it was excellent because it really made you "think" about your answer and critique it before you clicked that box. Mind you, they were not trick questions however they were written very professional and very plurable.
Btw, everyone does things differently state to state, country to country so that is something to consider. But do what will best work for your students and fit your's and their needs. I'm not sure if I answered any (or all) of your questions but giving you knowledge from experience. Hope this helps!