As far as I know, and mainly from neuroscience text books (not primary evidence such as original articles really), most cortico-spinal neurons do not end onto motoneurons directly, but on interneurons or premotor neurons which in turn innervate motoneurons. I guess by innervating an inhibitory interneuron/premotor neuron this phenomenon could be explained.

Not only Betz cells but also all corticospinal neurons establish direct and indirect excitatory connections with motor neurons that drive contraction of certain muscles (such as flexors) and indirect inhibitory inputs to motor neurons that drive the antagonists of those muscles (extensors). And so inhibition of the quadriceps comes along as part of the package for excitation of the leg flexors. The synaptic mechanism is through corticospinal excitation of spinal inhibitory neurons. Both glycine and GABA interneurons populate the ventral horn; they are specified by the gradient in sonic hedgehog during neurogenesis in the cord. Several populations of these inhibitory cells exist (one population called Renshaw cells gets motor neuron input and feeds back to inhibit the same cells); as a general mechanism the inhibitory cells see to it that excitation of a motor neuron population and those that innervate agonist muscles always occurs with inhibition of motor neurons for antagonist muscles. Dystonias occur when something (usually damage to descending systems) interrupts this coordinated excitation of agonists and inhibition of antagonists.

I agree with Stewart's comments. Betz cells are not inherently inhibitory, their input is actually excitatory on motor neurons of the ventral horn of the spinal cord. Inhibitory action (on antagonist muscles) can be achieved through inhibitory interneurons.

Can any of you provide published articles showing that Betz cells terminate on inhibitory interneurons? I agree with your perceptions that this is probably the case, but have no direct evidence to support the perception.