The trust that browsers place in the TLS chain of trust is basically just the assertion that the holder of the TLS key is the one who owns the domain. This doe

The trust that browsers place in the TLS chain of trust is basically just the assertion that the holder of the TLS key is the one who owns the domain. This doesn't imply anything about the contents that can be transferred over the TLS connection. Could be malware. The other side could leak your private data like crazy. That's outside the scope of the TLS chain of trust.