"it has been stated many times that his increase in FlL request was denied. It's highly unlikely that he would initiate a unauthorized climb to move up to optimum ."
He had been cleared to climb from FL320 to FL340 and to await further clearance. He shot through FL340 in the zoom. A 90 degree turn is not a w/x 'deviation'; it would need a PAN call or at least to advise how many degrees. It's normal to state how many degrees L/R, or more usually, the number of miles off track required.