Theoretically what you're saying is true, but practically speaking many websites are behind CDNs, like Cloudflare, Cloudfront or Akamai, with static content being cached aggressively to reduce costs and latency and it's pretty cheap and easy to do so nowadays, so most requests aren't even going to hit a backend.
You can work around this by installing a tracking pixel on every page you have, a pixel that always hits your backend, which can then generate a log line that can be analyzed. But this requires extra development and it's much easier to just install Google Analytics.
So I'm pretty sure that most browser stats are not coming from analyzing 1st party data that's logging the user agent.
And speaking from experience in this space, the error margin for such analytics is somewhere around 10% - 20%, which is roughly the percent of people having ad-blockers installed and this number is growing — you can extrapolate of course from those that don't have ad-blockers installed, but then you have a selection bias issue, because you're not talking about the same kind of user; e.g. people that use ad-blockers are the people that are more likely to be computer literate and capable of installing their own browser.