If these numbers were significantly changed by a server side page view, I'd bet their page view wasn't firing any earlier than the top or bottom of the body tag

If these numbers were significantly changed by a server side page view, I'd bet their page view wasn't firing any earlier than the top or bottom of the body tag, or maybe even on window ready. Anyone that's spent any real time outside of dropping in a snippet understands the implications of users navigating before hits fire, and it sounds like the team just didn't have that experience. Like you, I also work to make sure people understand that client side data is not necessarily accurate, but still refer to it as metrics and KPIs, just with the caviot that we should bank on consistancy over accuracy, keeping our analysis geared towards behavior and trends versus most business people's immediate desire to take it to an operational/business intelligence type place.