1. Your definition of PII. PII is defined in legislation in some states/countries, whereas other terms are used elsewhere. Some definitions are very loose, whereas for example, the EU definition of a close/equivalent (simply referred to as "personal data") is extremely strict (some might say too strict). If we take the EU definition, GA definitely collects "personal data" as it is 100% required to provide dashboard data on "unique visits".
2. Even if you take a looser definition of PII, by which Google could potentially provide all GA dashboard features without collecting any PII, you are still giving Google direct access to PII, and explicitly sending them some PII in some situations. So in this case, you're relying on your trust of Google's internal company policies on not storing that data that they receive. Given their track record in compliance with the law on data collection, there is very little reason to trust them.