First off, I don't understand how you make the jump from "wants a possession" to "deserves to be treated as a possession." Even if we accept that wanting a diamond ring would make her dumb (and I don't accept that), it still wouldn't warrant treating her like property. That seems like an awfully dehumanizing perspective to hold.
Second, the fact that the tradition is a modern one, that started with an advertising campaign, is basically irrelevant. As far as the woman is concerned, this is something that every other married girl she's ever known has received. It's perfectly natural to want hers too. If she's particularly financially minded or happens to be exceptionally grounded in this case, she might decide to reject the tradition, but it's hardly a marker of unintelligence to feel otherwise. I'm sure you hold many irrational preferences in your life, as do we all, and it's not any more fair to insult her for her wishes than it is to insult you for yours.
I find it interesting that you suggest a down payment on a house as an alternative to buying a diamond ring. First, you're presuming that the diamond ring is such a burden that it's getting in the way of the couple's other financial obligations (which may be the case, but also may not). But also, your suggestion proves just how subjective and emotional these things really are, because property ownership is yet another optional part of "the dream" that many might consider a needless extravagance, much like a diamond ring. Sure, it seems to have more utility (on the surface), but it's also far more expensive, and it will continue to become more expensive as time passes on. Property ownership is valued much more highly in some cultures than others, and the notion of saddling yourself with debt (a mortgage) for 30 years just for that privilege seems downright insane to some people.