This is false. I only browse reddit in the browser version on my phone. It annoys you all the time to install their app, but you can read and post perfectly fine.
Your rebuttal is false and the parent is accurate. Reddit will throw up a full screen interstitial on most popular subreddits preventing even viewing and redirect you to download the app. This is on the mobile (not old.reddit desktop-only) site. Their UX is shite and full of dark patterns.
If you log in, the mobile site is perfectly usable. You might also have to set a preference as well (like the old.reddit preference). It has been so many years of using it this way I don't remember.
You can on old.reddit.com. Their redesign was so unpopular with users they agreed to keep supporting the old design which doesn't nag you into downloading the app.