  We study the relation between the 300-700 Hz upper kHz quasi-periodic
oscillation (QPO) and the 401 Hz coherent pulsations across all outbursts of
the accreting millisecond X-ray pulsar SAX J1808.4-3658 observed with the Rossi
X-ray Timing Explorer. We find that the pulse amplitude systematically changes
by a factor of ~2 when the upper kHz QPO frequency passes through 401 Hz: it
halves when the QPO moves to above the spin frequency and doubles again on the
way back. This establishes for the first time the existence of a direct effect
of kHz QPOs on the millisecond pulsations and provides a new clue to the origin
of the upper kHz QPO. We discuss several scenarios and conclude that while more
complex explanations can not formally be excluded, our result strongly suggests
that the QPO is produced by azimuthal motion at the inner edge of the accretion
disk, most likely orbital motion. Depending on whether this azimuthal motion is
faster or slower than the spin, the plasma then interacts differently with the
neutron-star magnetic field. The most straightforward interpretation involves
magnetospheric centrifugal inhibition of the accretion flow that sets in when
the upper kHz QPO becomes slower than the spin.
