I always think this should be an incident in itself - why did our status page not reflect the reality of a degraded service? It's so common that they don't, and something user-driven like DownDetector is often more reliable
I don't think an accurate and automated public status page is something any management would want. If it was accurate they wouldn't be able to lie to customers about the uptime. So I always suspect status pages are adjusted manually.
That's exactly what happens. How we need to respond though is by not linking to status pages hosted by that party, instead we should be linking to a StatusGator or DownDetector page as a 'source of truth'.