That's just like your opinion...man, I disagree, I don't think the Dalish have any rights when it comes to the well. It's up for grabs. As in, it no longer belongs to them. Sure their ancestors built it but in a long forgotten age, that the Dalish have forgotten and misunderstood. So, no Op. I think you are wrong and the Dalish of today have no inherent claim on it.
I don't really agree with this - simply because someone has deeper knowledge of a culture doesn't mean one obtains ownership over that cultural heritage. It would be akin to saying since the British Royal Museum may have studied Chinese porcelain more deeply, it has a right to retain objects it forcibly stole/looted from China during the the European invasion that destroyed Yuanmingyuan. (Because Morrigan really does, in a sense, try to forcibly obtain the Well of Sorrows) I think it's important to understand that culture and knowledge, while they can be intertwined, have to be treated with differing attitudes - while knowledge should be open, culture is something for which there are certain limitations of ownership (see: cultural appropriation).
Also the ancient elves who built that well are there - Abelas - and they explicitly state that the Inquisitor, not Morrigan, is the one that they deem worthy of drinking from the Well.