Let's see what the sharia says about wudu.
I'll use use the Umdat since I have it open:
"e5.1 Ablution has six obligatory integrals :
(a)to have the intention when one starts washing the face;
(b) to wash the face;
(c) to wash the arms up to and including the elbows;
(d) to wipe a little of the head with wet hands;
(e) to wash the feet up to and including the anklebones;
(f) and to do these things in the order mentioned.
The sunnas of ablution are all its actions besides the above. (N: The obligatory minimum is to
perform (b), (c), (d), and (e) once, though the sunna is to perform them each three times.)"
Wow. Looks like all three of those hadith are correct. The muslim who would pray must do the ritual wash at least once (obligatory), and have the option to do it even more. No rejection necessary.
No doubt among the practitioner of Myslam things are different.
Hmm.. Almost as though the scholars of Islam, the jurists and such, I know it is difficult to believe, but well, they might know a thing or two...