I was asking because I'm currently nowhere near a system that I'd trust for this purpose. I'll be near one later and, if you're interested, I'll update the question with my findings.
There exists a system that you wouldn't trust to provide a good-enough answer to the question "Does the onion service still serve the same advertisements their website and mobile app do?" ?
What do you think an untrustworthy system is doing that would make it give a not-good-enough answer?
That's a clever question and the answer has a few parts, mostly due to the slipperiness of "trust" as a concept: I wasn't specific enough in my description of my own threat model (which makes sense, as my aim wasn't to explain the threat model but to cultivate answers from other folks). In short, I currently only have access to systems that are too costly to replace, if the site is under active attack. That's not to say that HN's comment section isn't also a risk, but it seems less of one.
I considered these actors before deciding to ask the question instead of immediately connecting directly: available computer systems, internet pipes, the NYT website, and the bevy of third party ad-services hosted through the website.