Turn around vs. turn back

[Rich7]

Test No. incompl/inter-34 "Story (3)", question 5

'You'll be like that one day' she continued, Just you wait'. I turned ......... to apologize.

(a) around
(b) back
(c) on
(d) against

Test No. incompl/inter-34 "Story (3)", answer 5

'You'll be like that one day' she continued, Just you wait'. I turned back to apologize.

Correct answer: (b) back

Your answer was: correct
_________________________

could it be now "turn around"
or not why?

[Torsten]

Well,

If you turn around you only move your body slightly to the side. If you turn back you actually return to the place you were before.

TOEIC short conversations: Negotiating a lower price