The proxy loads websites in a browser, so it is alive — and the account still will not connect through it. There is no contradiction: those are different tests.
Protocol
Telegram works over socks5. An http proxy that serves a browser perfectly is useless to it. Check the type before you check whether it is alive.
Ports
Telegram uses its own ports, and some providers block everything except 80 and 443. A browser never notices; Telegram fails immediately. The symptom is a hang until timeout with no clear error.
Datacentre addresses
Telegram knows the ranges of major hosting providers and treats them with suspicion. The proxy works technically, and the account behind it hits restrictions sooner. Residential and mobile addresses behave far more quietly.
Geography
An account registered in one country connecting from another is itself a reason for review — especially if the country changes between runs. Sensible rule: a proxy from the number's country, and a permanent one.
How to test properly
Test with an actual account connection rather than a browser: it is the only test that answers the question you have. One dedicated proxy per account — shared addresses link accounts together, and a restriction lands on the whole group at once. More on the automation page.