Rank of bait affecting rank of caught crabs?

[KoongFoo]

My wife and I are very excited about the new late game content and we are now enjoying Dave way beyond the official end. One question about the crab catch baskets: Does the rank of the bait used affect the rank of the crabs caught?

[VaeliusNoctu]

same question here i have 5 crabs that i cant get at rank 3 Star. The last thats not 3 Star Rated in my complete Marinca Set.

EDIT:
seems so i used after i read what you write a rank 8 fish as bait and get one crab that at rank 3.