What rights do you need for Ola's integrity check? I'm configuring a new server and Ola's integrity check is working for user databases (I have restored a database of around 50 GB for tests) and is failing for system databases. If I look in the logs it works for model and fails for master and msdb with The database could not be checked as a database snapshot could not be created...

The SQL Agent account is sysadmin. It works if I add the SQL Server and SQL Agent account as administrators of the Windows Server, so it's some rights missing somewhere. It's a VM running Windows Server 2016 version 1607, I don't have access to the Hyper-V host but it's probably the same version.

Same result with SQL Server 2017 and SQL Server 2014. Seems to be caused by Windows Server 2016, maybe some group policies settings.
This sounds like more of an issue with DBCC CHECKDB being run than anything specific to Ola's.

Since you're probably creating snapshots, the service account will need to have access to the database directory folders in order to create snapshots there. You could work around this temporarily by peforming a physical only CHECKDB as well.