I’m assuming that you have an account that was migrated from the former VMware web site since you say you’ve had the account for a long time. Migrated accounts didn’t come over cleanly for users that weren’t a corporate account. This “screening required” message is one of the problems that has happened because the conversion didn’t perform the screening needed for export compliance
You are correct that basic account users can’t open support tickets through the web site. But you can call Broadcom Support and ask to speak to a Customer Care rep to deal with a web site access issue (not a technical support issue on Fusion). That seems to be the only way to clear the screening block - trying to do anything through the web site to fix it doesn’t work.