Yes, you're right, I didn't explain that part clearly enough and only alluded to it!
I am guessing that within DSolve it is, at some point in the course of solving your original equation, using Solve to do some algebraic solving as, perhaps, a final step. And when doing this it is generating the warning message. As such, it's reference to Reduce is only pertinent to the internal step which, of course, you have no access to! So, there really is nothing Reduce-able that can be done with what DSolve provides, nor a Reduce-able alternative to DSolve.
In the case where you might have been Solve-ing an equation and directly generating the warning message in the course of that, then one might use Reduce. So, in the documentation for Solve there is this example:
Solve[x^(2 a) + 2 x^a + 1 == 0, x]
and it generates the warning message that you encountered. And then using Reduce instead of Solve one gets a richer set of solution possibilties along with the conditional statements that govern them:
Reduce[x^(2 a) + 2 x^a + 1 == 0, x]
So, in summary, in the original DSolve case of yours, the mention of Reduce is, I think, a red herring (i.e., fishy in a way) in that it does not give you direct actionable recourse. But it does hint that there may be alternative approaches to forming the original equation that may lay bare any issues or assumptions.
