Hi @tank13 - happy to help!
Local is not capable of pushing to or pulling from Flywheel without being properly authenticated with Flywheel inside the app. You can rest assured that your sites (and your clients and their info) are secure on Flywheel.
Your Local account (log in by visiting Local Hub, hub.localwp.com) and your Flywheel hosting account are not the same. This is definitely a confusing workflow, and not the first time we have heard users have questions about it.
Logging into Local Hub unlocks development features like Live Links and Cloud Backups where we need to associate a user and their site to their Local app. This ensures your backups are only shown to you, your Live Links URLs are unique to you, etc.
Logging into Flywheel, a separate account, is done in the Local Connect window. See my screenshot below. If you visit the Connect tab in Local, you will see that you can remain authenticated with Flywheel even if you are not logged into Local. Hopefully this makes sense and eases your concerns, but I am happy to answer any questions you have.