I left another comment with the minimal example, but intuitively:

- proposers descend from their 1st choice, while recipients ascend according to their offers; the outcome can't be recipient-biased, because recipients ascend only when proposers are forced to descend

- a matching is stable if each pair contains at least one party that cannot find a strictly better match

- in particular there are multiple distinct matchings, and if proposer-biased, recipients have no recourse to break the proposer-favored pairs