It gives higher resists, but if the character doing the attack gets a better roll after all the numbers are added that includes tenacity, well, the debuffs will still apply then. Just means they got a very more luckier roll than the character being attacked.
REX has a killer tenacity up. It removes any debuffs on all your characters and stops any from sticking for a few turns. It's still bugged as far as turn meter and non clones, but still a great weapon.
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I would think it would stop TM reduction but I just saw Yoda with tenacity up get TM reduced by a stealthed teebo.
Haha