Where did you see the Dan Burn incident? As you say, MoTD didn't show it and I had a quick look on YouTube but couldn't find anything. From what I've read (inc on Everton fan sites), Burn was rightly booked for being a dick.
The difference between the Burn and Martinelli incidents based on what I've read (with the caveat that I haven't seen it myself) is that Dewsbury Hall went down on the pitch after a foul in just a typical way, whereas Conor Bradley's injury wasn't because of a foul and he was clearly in a bad way (i.e. this was clearly a real injury and not just a tactical going to ground), and Martinelli (a) threw the ball at him, (b) tried to shove him with his knee, and (c) then tried to push him off the pitch while Bradley was CLEARLY in real pain. It sounds as though Burn tried to pull Dewsbury Hall to his feet, which is definitely out of order. But, if what I've read is correct, Martinelli's behaviour was much worse and the scale and circumstances were much more unusual than the Burn incident. The latter was a more common occurrence. Both players were absolutely in the wrong, though.
I don't think the MoTD decision not to show the Burn incident was some sort of anti-Arsenal thing. The greater focus on the Martinelli action was because (a) from the sounds of it, it was much worse (not least because Bradley had suffered a season-ending injury), and (b) that match ended 0-0 so there was far less other action for reports to focus on, compared to the action-packed Newcastle-Everton match with 5 goals. Even Evertonians don't seem to be overly bothered about it, which is quite telling.
So, ultimately: from what I have read (but not seen) both players were out of order, but one even more so than the other.