>> There's not a man I meet but doth salute me. As if I were their well-acquainted friend > Singular 'they' even when the gender is known has been popular in t

>> There's not a man I meet but doth salute me. As if I were their well-acquainted friend > Singular 'they' even when the gender is known has been popular in the English language for hundreds of years. Even longer than singular 'you'. It seems to me that the negation qualifies your Shakespeare example for OED's explanation of "I. 2. Often used in reference to a singular noun made universal by every, any, no, etc., or applicable to one of either sex (= ‘he or she’)." That is distinct from a reference to a single, specific individual, which using "they" as a singular gender-non-specific pronoun with unrestricted usage would necessarily include (things like "Peter said *they wanted some tea"). Presumably this is what was meant by GP.