Does the Card take the place of Perplex?
I know that sounds odd so I will give an example

Example-
Mr Fantastic perplex's an enemys Def Down
and then perplex's the Thing's Att Up.

We had this happen at an event. The FAQ wasnt very helpful in this case.

Could Mr Fantastic still use his perplex in that manner when using the card?

You're interpreting it right. If Mr. Fantastic has Brilliant Tactician assigned to him and is on a Perplex click, then any time he uses Perplex for any reason, be it to perplex an enemy's defense down, perplex his own range up, perplex the damage of a non-Fantastic Four member up, whatever... he gets to also use Perplex on any Fantastic Four members (or wildcards mimicking the Fantastic Four ability) that he has line of sight to.

This is why I love Brilliant Tactican. It can really go a long way towards helping to hit those super high Defensive Values.