1 250mb internet download vs. 4-8mb for a couple hundred machines on the internet line is a big difference. Particularly since I can plan when the big download happens (and update) versus all the small downloads that happen in a lab at the same time because of a class starting. Students with the first class of the day don't feel terribly happy about being the designated updater of some company's software.
Make that a few kb. And last time I checked at my work, admin updates usually happen during work hours and affects people working in the "lab". Also, it's 1 250mb that is sometimes installed on each machine on the network, so way worse than a few kb.
Your admin is doing it wrong if updates of a few kb are clogging his network. Also, small labs can't afford to pay admins at night, and big labs surely can afford a few kb transfers on their networks. We're talking about gigabytes networks and admin can always use cache proxy so that chrome only taps the net once for the tiny kb update.