I came through GRU the past week headed to POA and I had a similar experience.
The customs agent for foreigners wouldn’t accept just the medical insurance card, he needed to see coverage of at least 30k BRL.
My Portuguese isn’t great, but showed The online policy with deductibles (adding up to $30k+ USD) with my name and that was sufficient. I’d recommend printing out, since the WiFi in the customs area can be spotty.
Do ensure all documentation is in English and/or Portuguese, as they don’t accept Spanish, for example.