The story has been concluded - finally.   I don't want to let you hanging...

On May 26, I left the bike at the mechanics.  
After a couple of days the mechanic diagnosed the problem as:  bearing on the drive shaft, inside the crankcase.  
It took a long time to get the parts...

I got my bike back today.  I rode 65-70mph - no vibration.  It looks like the diagnosis was right and the fix was proper.  
 

It makes me wonder...  I haven't heard that the bearing on the middle drive was a common problem.  But - is it?  Maybe some of the broken shaft problems (not all) come from the broken bearing and the vibration... otherwise the screw wouldn't unscrew.  
What do you say?

That's the first time I've heard of one going bad. 

That's a 1st for me as well.

Quick Mick and Donn,

Thanks you for your quick answer.  
I, myself searched and re-searched and haven't found any mention on the Internet of this.  But, this is what it was.

Now, I always ask a question - could it be prevented?
I am a one-year-old rider, but I am a gentle rider.  No racing, no wheelies, no tire burning...  So, was it just a defective part?, or it's an underlying problem deeper in the engine?
As of today the bike has 9340 miles on it.  It's a baby (16 y/o baby - but a baby).

Being a non-serviceable part, I don't know how it could have been prevented and it sounds like yours is a isolated case. When I had mine I rode it hard, no wheelies but I did race a bit and maybe a couple of burnouts. :)      

Yeah.  It looks like an isolated incident.  Summer is up.  I am going to put some miles on the odometer...  Hopefully, there are not too many 'isolated incidents' stored for me in the future.  I am not trying to be unique... I am not trying to stand out in the crowd... I want to be like everybody else...  Just wear and tear up to a 100k miles. Ha Ha Ha.   Cheers.