I heard the audio recording of this witness on CNN, played right after the event.
It sounds totally credible and I see no reason to doubt the veracity of this witness.
Saying “Allahu Akbar” while shooting infidels is decisive evidence in favor of an Islamist motivation. Only total morons or politically correct liberals could doubt this. Ok, that was redundant, I know.
When police or govt officials and/or the media look for “ties” they up the bar to demanding some conclusive evidence that a terrorist has been pledged to a specific group such as ISIS, is under command of some terrorist mastermind, etc.
What this episode would seem to show (like Orlando, Nice, San Bernadino, etc.) is that there are plenty of willing jihadists who will mass-murder on behalf of Islam. Whether or not they claim some official affiliation(s) with organized groups is far from the main or only question.
What's significant is that he was an Iranian-German who held dual citizenship, and that the shooting was not a rightwing reaction to immigration, as some persons had suggested. On the other hand, the claim that he shouted "Allahu akbar" is doubtful, to say the least.
The claim stems from the telephone remarks of someone identified only as Lauretta. She was found soon after the initial attack when a reporter called businesses in the vicinity of McDonalds in hopes of finding a witness.
I'd like to believe what she said because it serves the cause of anti-Islamization, but she makes several claims that bring her testimony into question. 1) That her son saw the shooter loading his pistol in the bathroom, and that she herself was only "two centimeters" away from him when he started shooting. That's possible, but unlikely.
As for the loading, the shooting hadn't started yet. Why wouldn't he have brought his gun from home already loaded? And would he have started shooting with someone just "two centimeters" away, and possibly in a position to subdue him (or, at least, impede him enough to allow others to do so)? I doubt it.
2) Most important -- she claims that he shot children inside McDonalds -- "the children were sitting to eat". As far as I know, no one was shot inside. A video shows him standing outside, in front of McDonalds, and firing at people who are approaching. If anyone has information that bodies were found inside, please post it. Until then I'm forced to assume that her story is a fabrication.
Two CNN YouTube videos (each contains part of the story): How the supposed witness was found, "Allahu Akbar" claim.