I think there's a key point in here about some phraseology leading to ambiguity. In effect there are two lateral modes for an aircraft under an ATC service: maintain a heading mode, or own navigation, in which the aircraft is free to make heading changes to maintain track. The aircraft needs to know what mode is agreed.
Consider some of the following:
1 "Turn left 30 degrees and maintain that heading"
Clearly maintain a heading mode
2 "Turn left 30 degrees and make that a radar heading"
OK, we don't like the phraseology, but still clearly maintain a heading mode
3 "Turn left 30 degrees and report your heading"
Probably still maintain a heading mode, but less obvious, I think.
4 "Own navigation direct XYZ"
Clearly own navigation mode.
5 "Route direct XYZ"
Still probably own navigation, yes?
6 "Route direct XYZ and report your heading"
Er. Well by analogy with 3 we're in maintain a heading mode. By analogy with 5 we're in own navigation mode.
So in case 6, if I find myself diverging from direct track on that heading, do I turn to maintain the direct track or do I maintain the heading I read to you?