You can certainly play covers and have artistic integrity! Try telling a world class orchestral musician that he lacks artistic integrity because he plays "covers" of Bach and Beethoven!
That's a great point.
In this case, his "integrity" is playing faithful renditions of popular classical pieces.
And that's exactly what some of these bands augmenting their sound with tracks are doing; playing popular, classic songs as faithfully as possible. So, in that sense, it's the same kind of "integrity" or "faithfulness" in place.