Bioware is no longer the Bioware from DA:O times; they might have been able to convince EA to not use Frostbite in the first place, but once that decision was taken, they now have to follow EA to the bitter end.
EA are encouraging all their developers to use Frostbite by giving them more budget for their games, that combined with the fact that they didn't have to pay for an engine would've meant alot less budget for BioWare to develop DA:I.
Their old engine needed an update and they weren't going to get the money from EA to do it while EA had Frostbite, so if they hadn't of made that choice who knows what DA:I would've been like.
With less money towards development though, it probably would've been as good.
Well, Terodil's right that this is all internal EA stuff, since both DICE and Bio are wholly owned by EA. Though disputes and different goals between branches of a corporation are a real thing. I've lived through a few of those in my time.
Depending on the regulations that affect sister companies in EA, they may only be able to share certain things.
I work in a similar situation and there is shockley little data that some of our sister companies can share with us, due to a whole host of regulations.
Also since BioWare & DICE operate as separate companies (even though they are both owned by EA) there could still be copyrighting & licensing issues between the two. For example; if Frostbite is copyrighted under DICE instead of EA, the this could affect what BioWare can do to it.
We ran into an issue like that, one of our sister companies had developed a tool we wanted to use, but we had to modify it, and there were lots of issues we had to work through to both be able to use it and to modify because it was copyrighted by our sister company rather than our parent company.