Blues and country were the core of rock. And as rock grew legs in the 60ies it looked at some of its roots more closely and bands such as Buffalo Springfield, The Birds, Gram Parsons or the Nitty Gritty Dirt Band took on board country influences while bands such as Ten Years After, Chicken Shack, Fleetwood Mac and Canned Heat looked closer at the blues. Some bands looked at both (Rolling Stones).
For a long time there seemed to be a greater influence of country on rock than the other way around, I remember bands as diverse as Crosby, Stills, Nash & Young, The Band, Flying Burrito Brothers, Linda Ronstadt, Emmylou Harris, Eagles, Poco and even America or Dr. Hook & The Medicine Show all being referred to as "country rock" here in Europe in the 70ies. And some bands played country tunes where you would haver never thought it:
But come around the 80ies and 90ies, rock had become such a prevalent force in popular music that its influences started running into country music - and that led to the emergence of New Country in which I hear traces of U2, AOR (of the Journey, REO and Foreigner type) and even LA pop/hair metal.
And I don't think it is necessarily a bad thing - it certainly has dusted off country music on one hand and raised recognition in rock quarters where that music initially also sprang from (other than the blues).
The discussion whether a piece of music now qualifies for "real" or just "new" country does remind me a bit of the furor Herr Zimmermann caused when he strapped a Strat around his shoulder at the Newport Festival in the early 60ies and was all of the sudden no longer perceived as a folkie by the diehards. Incidentally, I'm seeing him on Friday once again and he will no doubt be shifting from country to rock to folk to blues effortlessly from song to song.