Hold the phone, joan! There was a flaw in my test.
The K-5II was set to Contrast AF for Liveview while the K-r (I just discovered after going back again) was set to Phase Difference AF!
After I set the K-r to Contrast AF and tried again (same spot) with the 16-50, it is all over the place with what it thinks is correct focus too (at 95feet away from the flat, brick pylon).
To cross check, I configured the K-5II to Phase Difference AF and it no longer bounced around infinity with this 16-50.
So what does this tell us?
---------- Post added 12-12-15 at 02:40 PM ----------
Full sized example shots on the K-r:
Both shot on a solid tripod in Contrast AF, single focus point (aimed straight at the brick pylon front and center), 16-50mm @ 50mm f/2.8
Push the shutter half way, until I hear the camera beep, then press the shutter button and wait for the 2 second timer to click off a shot. Then redo back again. And mega blurry. The closest lounge chair seems to be almost there.
This is what it does on both cameras.. hit or very miss. And even when it does hit, does that look really sharp for infinity at 2.8 with this lens? Still seems rather soft to me..