Hello @Dimitry 
Can you please check two things for me. 

1. Register the Event Grid Resource Provider: to check this go to subscription > Settings >Resource providers>event grid is registered or not?

2. 403 error is more of no connection actually, its strange that you are able to read the file. 

For this. can you confirm on the Firewalls and virtual networks of storage account. check whether you have. checked : Enabled from selected virtual networks and IP addresses

these are my findings. I hope others have any solution for this issue.