The kinetic coefficient μk is always smaller than μs (or else an object would never slip because it would "stop slipping the instant it starts slipping")
The claimed conclusion is not true. Obvious counterexamples include:
A boat in the middle of a lake. The static friction is zero for all practical purposes. The kinetic friction (i.e. drag) is vastly greater for all speeds of interest.
A cart on an air track. The static friction is zero for all practical purposes.
An ideal rolling (as opposed to sliding) object.
et cetera
Given that the conclusion is wrong, the explanation (in parentheses) must also be wrong. The explanation seems to assume that the kinetic friction is strictly independent of speed, which simply cannot be true. For starters, it cannot be independent of speed near |v|=0, because otherwise the whole concept of static friction would be undefinable.
One could possibly get away with arguing that the limit of the kinetic friction must be less than or equal to the static friction, in the limit as the speed goes to zero. However,
This only applies in the infinitesimal neighborhood of |v|=0; otherwise all bets are off.
The "or equal to" case is often the relevant case ... probably nearly always the relevant case if you look closely enough.
The limit is not always approached from below. For the boat, it is approached from above.
In section 10.10 on page 252 it claims:
The claimed conclusion is not true. Obvious counterexamples include:
Given that the conclusion is wrong, the explanation (in parentheses) must also be wrong. The explanation seems to assume that the kinetic friction is strictly independent of speed, which simply cannot be true. For starters, it cannot be independent of speed near |v|=0, because otherwise the whole concept of static friction would be undefinable.
One could possibly get away with arguing that the limit of the kinetic friction must be less than or equal to the static friction, in the limit as the speed goes to zero. However,