The post office does own your mailbox even if it's a mailbox you've bought and installed yourself.
Once you install the mailbox and declared it as your USPS delivery point the mailbox also becomes federal property but you still also maintain ownership of the mailbox.
You are still responsible for maintaining your mailbox but your mailbox is also protected under federal law.
Putting anything into someone's mailbox without it having a proper stamp and going through the USPS is illegal and can get you into trouble including a fine.
By law, only the USPS can place things in someone's mailbox once it has gone through the postal service and has a stamp or postage on it.
Never place anything inside someone's mailbox including letters, flyers, advertisements etc.
Even opening up someone's mailbox without the persons permission can be a federal crime.
Mailboxes are considered property of the USPS even though the homeowner has bought and installed the mailbox themselves.
Mailboxes are protected under federal law through the USPS.
Even damaging mailboxes can get you arrested and charged with a federal crime if caught and convicted.