Not necessarily. Remote exploits, definitely, but entirely local jailbreaks that require booting the phone into a specialized firmware-loading mode don't actually impact the user's security, just Apple's anti-tampering guards against the user.

Wrong. The first jailbreak was done because the iPhone trusted the restore mode commands coming from iTunes. The protocol was totally reworked so that the iPhone would only run some canned scripts. This did nothing to improve device security (it pretty much only enabled the jailbreak), but Apple fixed it fast.