If Itachi didn't kill Shisui, how did he really awaken his Mangekyou Sharingan?
The Mangekyou Sharingan is activated once its user experiences great loss, especially of someone close to him.
This means that Itachi did not have to kill Shisui in order for the Mangekyou to activate. What is most important for the activation is that the user feels the loss, which causes their brain to release a special kind of chakra that affects their optic nerves (chapter 619), thus awakening the Sharingan, and the Mangekyou, depending on what 'level' you were before, and on how much loss you have experienced. The more loss you experience, the more powerful the Sharingan gets.
Probably, just witnessing Shisui's death to protect the village was traumatic enough for Itachi to awaken his Mangekyou.
Also, if you remember, Sasuke's Mangekyou activated when Itachi died. He did not kill him either, but witnessing his death, even though he hated him, was traumatic enough to activate it.
That may be true, but that's not how Sasuke got his Mangekyou Sharingan. In the episodes following the fight, we learn that Itachi implanted his Mangekyou powers (Amaterasu, etc.) into Sasuke. Those powers activated when Sasuke looked at Madara's Sharingan; as Madara explained, Itachi made the abilities self-activate when they came into contact with Madara's Sharingan. This was because Itachi did not want Madara and Sasuke to meet, in order to prevent Madara from telling Sasuke the truth about Itachi.