Now Hillary!'s opportunistically-variable accent is drawing attention....
I note that my own accent is unplaceable and inconsistent. Just yesterday, someone asked if I was Canadian - something about how I was pronouncing my Rs at that moment.
Here's the thing: in the modern age, one has many influences, not just the local sounds of one's birthplace.
My base accent is Bay Area. All those tests with groups of words that sound kinda-sorta alike but people from different regions pronounce them a little differently? By default, I pronounce them exactly alike.
Then there's a Great Plains overlay, from my grandfather (my father doesn't have that accent so's you'd notice it).
Then... well, there are further overlays of Mel Brooks, and Monty Python, and Pogo, and German opera, and Irish folksingers. Lately, Slavic influences have been creeping in (thanks, Internet!). And, last summer, after about three days in Tennessee, I found myself slipping into local pronunciation at times (the Appalachian accent is highly contagious, and I'm a bit of a chameleonic lifeform to begin with).
A variable accent isn't necessarily an intentional effort to pull the wool over the rubes' eyes (though with a politician, that may be the way to bet). Sometimes it's just unconscious drift, or response to local influences.
Now, should I find myself adopting the rural life next year, I might just dial up the West Country and look for a sample of Comic Rural Ukrainian to add to the mix....