It probably isn't so simple one way or the other. The Open Skies document alleges that the AD government paid the sponsorship, which is where the ADEC thought comes from, I think.
But, at the end of the day, both can be true. 8 million could be paid out of the cash resources of Etihad and the remainder could have been forwarded from ADEC to Etihad specifically to fund the sponsorship. So Etihad would have paid all the sponsorship as Pearce said, but the vast majority would have had to be arranged from ADEC, as the emails said.
Context is everything.
Edit: And if the allegations are anything like UEFA, they aren't questioning that Etihad paid the full amount, anyway. The allegation is that the majority was funded into Etihad by ADUG/ Mansour for which, I expect, they will have no evidence at all.