You need to be able to say "We have this thing in our office pinging your API, and it was down for the last 96 minutes, therefore pay up!"
If you don't chase the company and present evidence, they won't pay for their own SLA violations.
The companies own status dashboards usually don't have sufficient proof to claim. "We are investigating reports that some customers may be encountering connection difficulties" isn't enough info to prove that you were seeing downtime.