Yes, water is a stronger base than say, hypochlorous acid, that's why water can pull the proton off HOCl, which is why we call HOCl -- hypochlorous
acid.
I'll admit 'tho, that water is a stronger base than hydrogen peroxide leaves me a little bit confused, does H
2O
2 really lose a proton in aqueous solution? The numbers are there in your question, but the concept is a little far out for me. So I do understand your confusion.