As suggested above, I wouldn't take a city employee "voice on the phone" as very credible. Surveyors have a standard they are generally loath to forgo (for very good reason) and they have a license they want to keep. I doubt they would seal a drawing that was worked from a questionable method, but maybe I'm naive. I find it odd that an anonymous city voice would cast dispersion on a professional surveyor without more substantial data- seems inordinately unprofessional.
My experience with different cities is that you can get all kinds of verbal approvals over the phone and in meetings, even across the table in plan reviews, but those evaporate when you apply for permits. Permit reviewers and local Fire and Rescue don't feel bound by an earlier verbal approval especially one over the phone.
I would talk to your surveyor and clarify in detail first, before doing anything else cause this city response sounds kinda like BS. Then I would get sufficient sketches and notes together and meet with a permit reviewer before I proceeded very far.