...so I don't see why Emma "couldn't" (as opposed to "wouldn't") under the right circumstances.

I look at Mr K & Martin as sort of a boss-employee relationship, in which the two parties, although they can never be truly intimate due to their different positions, are friendly, with affection and mutual respect, and enjoy each others' company when called to discuss business, and sometimes even personal matters (it's clear that Martin has somehow let Mr K know how he feels about being turned down).