This theory draws its basis from fact but then requires a leap...
English explorer Martin Frobisher (circa 1535 or 1539 – 1594) is well known for his efforts to find the fabled Northwest Passage. In the process, he was also instructed by the Queen to find gold, largely to cover the costs of his voyages. On his second voyage to Frobisher Bay in 1577 he carried 200 tons of ore home on three ships. Encouraged, he returned with an even larger fleet and dug several mines around Frobisher Bay. On this voyage he returned with 1,350 tons of ore.
Unfortunately, during the smelting of the ore, it was realized that the ore was iron pyrite. Therefore, almost worthless.
Frobisher did also take on the role of an English privateer/pirate. In so doing he plundered riches from French ships and was later knighted for his service in helping to repel the Spanish Armada.
The connection of these Pyrite mining expeditions in a different part of Canada to Oak Island seems tenuous at best.