Of course it could just as easily drive the average up, but the point is that it's a hedge: it's accepting a reduced chance of possible higher returns for the safety of reduced chance of possible lower returns.
If you commit to the strategy (buy monthly for 10 months) then you're just choosing an unknown price over a known price.
And if you don't commit to the strategy, then you're actively trading and not DCA'ing.
Another thought: if the thesis is that the price will go up, then whatever sum you have and want to invest, should you invest it all now - given that the price is supposed to go up?
A financial hedge is, generally, something which reduces risk or improves on the risk:reward ratio in a mathematically demonstrable way. Generally this means bundling uncorrelated (or anticorrelated) assets. This concept won a Nobel for Econ in 1990(?), and is the foundation of modern portfolio theory.
Using "hedge" in a more colloquial way, it can mean "a way to protect yourself from an unexpected poor outcome". But by that definition this also fails, since you're just as vulnerable to outlier events, but the nature of those outlier events is different (and perhaps less intuitive).