If it stays on your device, encrypted, it is safe from unauthorized access, and your privacy is assured as it is also anonymously randomized. I don’t expect everyone to understand the technology involved, but it should be easy to get that storing your stuff on a server on the internet, is the LAST THING ANYONE WOULD WANT.
http://appleinsider.com/articles/20/05/07/european-countries-form-coalition-over-contact-tracing-app-concerns