Interest rates, inflation and liquidity effect
The reason why supply effects would not occur is the result of market efficiency assumptions: all financial assets have the same expected returns. Within the bond market, that would imply that the "term premium" is zero. 

If the term premium is zero, then:


The value of the 1-period "bond" is the result of the central bank reaction function. (The policy rate.)
The value of a 2-period bond is determined by the 1-period yield, and the unbiased expectation of the 1-period yield, 1-period forward.
(Build up rest of curve similarly.)


They added market segmentation as a way of allowing bonds to trade away from the predicted ('efficient") value, that is, allow a non-zero term premium. Once we allow for a non-zero term premium, supply effects can be seen in predicted bond pricing.

The term premium interacts with supply as a positive term premium will induce bond investors to increase the holdings of bonds relative to the allocation that would happen if the term premium were zero. That is, changes in the term premium is needed to balance the market.