Typical flawed logic...
Just like artificial reefs, oil rigs only concentrate marine life by pulling it from the surrounding environment, thus making it easier to harvest. Naturally, this concentration of marine life would then attract large game fish too.
I'm not sure your argument holds water - would you say that coral reefs just pull in marine life from the sand around them? Pretty sure the answer is no.
By making an environment where fish can sleep and raise their young in some safety (more safety than on a muddy/sandy featureless bottom) I think life can and does proliferate around artifical structures.
There are tens/hundreds of places I've dived where human intervention (deliberate or not) has clearly enriched the amount and diversity of life in the ocean. Some examples range from big - piers, flood guards and shipwrecks to small - boxes, bottles and boats. I can't see any reason a decomissioned oil rig would be any less habitable than a shipwreck.
If you had dived in somewhere like Truk lagoon you would see how the wrecks there are an absolute haven for hard corals, soft corals, young fish, reef fish, predatory shoals, sharks etc etc. The argument that they would all be just hanging around in the sand if the wrecks weren't there is completely wrong in my opinion.