I’m always surprised that people can’t rephrase their sentences when someone doesn’t understand. How hard is it to say “oh no, not that kind of complaint! I mean symptoms like coughing or sneezing or a headache”.
As to what is good English? Consistent pronunciation (that’s what Hansen teaches). Everything else is negotiable, but decoding an inconsistent accent is very difficult for anyone to understand. And it’s not specific to non-native speakers… plenty of native speakers don’t use consistent pronunciation and it’s sometimes difficult to decode what they’re saying.