Coincidentally, I found out while researching this topic that thiaminase is used in cancer therapy. Who knew?

This first one is a lame reference for this topic, but mentions that some fish have more thiaminase than others, and that feeding frozen fish of any species is more problematic than raw.
Wilkinson, Stacey Leonatti. "Reptile Wellness Management." Veterinary Clinics of North America: Exotic Animal Practice 18.2 (2015): 281-304.

This reference is an example of a specific fish species that can cause vitamin B1 deficiency when fed to alligators. With reference to wild populations I "assume" they are talking about feeding fresh raw fish and not frozen.
Ross, J. Perran, et al. "Gizzard shad thiaminase activity and its effect on the thiamine status of captive American alligators Alligator mississippiensis." Journal of aquatic animal health 21.4 (2009): 239-248.

This reference states that certain fish, namely those related to herring or smelt (potentially ignoring fish species not used in aquatic bird management) are richer in thiaminases than other species. It also refers, and this perhaps refines my understanding of the issue, is that there are certain bacteria that produce thiaminase (which concurrs with my literature search but I previously thought was an unrelated tangent). How this relates to fish is that fish goes rancid very quickly, and even in the freezer (one paper recommended -18C storage and even then there was progressive increase in thiaminase), thus this bacteria produces thiaminase very quickly. To further the problem, fat soluble vitamins (like vitamin E) are destroyed very fast as the fish breaks down which adds another nutritional deficiency to the problem.

Pokras, Mark A. "Captive management of aquatic birds." AAV Today (1988): 24-33.

...

So in the end, I'll be completely up front and say that I ignored one issue by attending another. Some fish do have enough thiamine to cause problems. Are rosy red minnows and goldfish these species? Likely... I've seen more information on the goldfish than the minnows but none that has come from the primary literature.

My original point should not be lost however as it is equally valid. Any fresh fish species is nutritionally superior to frozen fish, and this is regarding thiaminase and other nutritional components. Of course the caveat to that is concerns over parasitism. However knowing that frozen fish is less nutritious should give you the advantage while developing a menu for your pets.

I think that it is important to see that the specifics are unknown and not many people are looking for answers because the problem has been solved. Zoo's supplement thiamine in true piscivorous species, garter snake keepers feed a variety of prey to counterbalance any deficiencies of any one item. So nothing ground-breaking here, but a lot of food for thought