What facts prove that it couldn't be Zangetsu? I don't want to scrounge through multiple posts trying to piece all that together.
As for my argument for why it could be Zangetsu?
First, as has been pointed out before, Zangetsu refers to a hilt that is the same shape as the one Ichigo originally carried as ME. That signifies that it should be Zangetsu. This is also the form it took before Ichigo knew Zangetsu's name.
On another point. Zanpakuto are an inner reflection of the Shinigami themselves, a part of them and their power. While Rukia did place her own power into Ichigo. If you think back to right after Ichigo got attacked by Byakuya. Urahara states that while he destroyed Rukia's power, Ichigo's own Shinigami power was able to hide.
For it to hide it would have first needed to be out. This means that Ichigo's power, where Zangetsu comes from, was active during the time he was using his Zanpakuto.
So is this sword merely the sealed state before Ichigo was able to achieve shikai? The only other person who seems to have a perm release shikai is none other than Kenpachi, and he doesn't even know his Zanpakuto's name. This means knowing the name of your Zanpakuto is not a requirement for having it in its shikai state, only using its shikai power.
So then, what is the sword Ichigo is carrying around then? Obviously he is able to channel a great amount of power throw it as shown by the little bout with Ishida. This would suggest it would have to be his own Zanpakuto, and not Rukias. Or at least give reason for it being that.
But it is still not necessarily just the sealed state before shikai either as evidenced by Kenpachi. So what?
I think that lies in what started the whole thing. Ichigo was original jumpstarted as a Shinigami with Rukia's power. It allowed him to achieve his own Shinigami power, but he was still relying on Rukia's power to jumpstart that. It seems that unless he was pushed hard, he didn't pull too much of his own power.
Basically what I am suggesting is that what the sword is, is Zangetsu being sealed because Ichigo relying on Rukia's power.
Think about it, to activate one's Shikai, one must use their own power as it is a reflection of their interaction with their Zanpakuto.
This means Ichigo's power, his Shinigami power, was being supressed by him relying mostly on Rukia's power. Hence why he did not immediately release into Zangetsu's Shikai form. Instead it was sealed off into the form we first witnessed. It would explain why his sword is similar to Rukia's, but would also mean that it would still be Zangetsu, just not a full realized one.