Cheers @codinghorror …
This is bringing back memories…
It seems I did this - as system user had been created and sent me a message or similar - so I just specified system in this setting.
There was no mention of how messaging / notifications / emails would be handled - or that I needed to specify an email address for the user. So a messaging update / consideration would be good 
Gees @cpradio (nice to see the passion in your writing) … of-course they are different - but they are also similar in terms of there possible abuse by unverified (TL0) users / spammers / bots. And this is perhaps something that should be considered as a part of this conversation.
Actually I have this problem - quite frequently - although the good majority of my users (for a specific forum I am thinking of) are only used to Facebook and phpBB and are in an age group (in the higher end of 35 to 58) which means to say they do not pick up on technology that quickly.
These users are also unable to to easily ask a friend for help - because their friends tend to be more behind than them.
I will concede that my initial thought to fix my problem was just to put in a Private Message button next to New Topic… I haven’t has yet taken any action but have noticed the PM frequency of PM’s has gone down slightly since switching from phpBB for the specific forum I am thinking of. I’m still considering if any action is required.
Yes TL0 users not being able to PM are another thing to consider in this mix.
For me I hate having to click a users avatar to PM - mainly because it takes ~3.5 seconds to load the user card after a click as an admin - but that’s another problem.