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FBI Extracts Suspect’s Deleted Signal Messages Saved in iPhone Notification Database
(www.404media.co)
This is a most excellent place for technology news and articles.
By not having Google Play Services, isn't this prevented?
If you don't use Google Play Services, you don't get push notifications, so yes. Libre reimplementations of Google Play Services such as Gapps etc. or alternative push notification providers do not circumvent this issue, except possibly self-hosted push notification providers. This approach is really rare though and limited generally to very few apps.
Is this true if you don't have Google Play Services but the person you're messaging does? Is one person cutting GPS out enough?
The message you send them would probably go through as a push notification to them, but the message they send you wouldn't.