I've been doing some more research, and it looks like if the partner is a spouse (in turn: spouse gains freedom of movement too), then Schengen law appears to guarantee use of the EU/EEA/CH lane, see article 10:
https://eur-lex.europa.eu/legal-cont...6R0399&from=EN

Which doesn't really tell you much about non-spouses, but on a practical level it doesn't seem likely that they'd be asking for marriage certificates.

But if anyone has actual datapoints, I would love to hear (theories aren't particularly helpful).