I would guess the second option there. Career chips haven't really been a big deal throughout the series ...
Yep, after all, Fry didn't really need one to become a cop, nor did Leela need one to sell real estates.
One question in this forum here brought me to that career chip question. I unfortunately seem to be unable to find it anymore, but it was basically "What is a starship captain certificate good for, when Farnsworth can pick anyone at random to be (new) captain?"
Little OT, but I somehow liked the underlying tragic in that, regarding "Leela's homeworld". She was supposed to play an example for the orphants (made something out of her life), when in fact it was not really a big deal to obtain that title.
And that character considering getting this rather meaningless title in exchange for never knowing her parents (quite an unfair deal) did somehow add another mean, tragic twist to her sadness in the locker room...(I doubt this was the writers intention...but yet...it seemed somehow fitting).