TL;DR : Yes, Fury hired them. Fury wanted the data without anyone KNOWING he had the data.
Prior to the beginning of the film, Nick Fury had reason to believe that elements within SHIELD - possibly even the World Council itself - had been compromised. While he had no idea the corruption was as widespread as it was, he still had reason to doubt whether or not anyone could be trusted, even upper-level agents like Natasha. We have no idea what evidence he found that caused this suspicion, but it's possible that he only trusted two people at that point - Maria Hill and Phil Coulson. Even then, he kept things as compartmentalized as possible:
Even fully trusting Coulson, Fury did not reveal his faked death to Phil until after the events of the film. He did, however, authorize Agent Koenig to reveal that information when the time was warranted. The exact nature of the Koenig "brothers" is still unknown, so they may not qualify as actual people (current evidence indicates they may be Life Model Decoys (LMD), aka androids.
It's also important to remember that Nick Fury is a sneaky SOB even under normal conditions. To quote Tony Stark, "he's THE spy. His secrets have secrets". When he suspects something is up, he gets uber-sneaky. He wanted to get the data being carried by the Lemurian Star, but wanted to do it in such a way that no one within SHIELD knew he had the data. His suspicions turned out to be warranted, as
Agent Sitwell, the agent in charge of the Lemurian Star operation, turned out to be a mole for HYDRA. Any requests for the data that went through normal channels would have certainly gone through Sitwell.
To get around this, Fury hired the mercenaries to hijack the ship, then sent in a team to "recover" the ship. Sending either Hill or Coulson would have looked unusual, so he was somewhat limited in his options. A team lead by Natasha & Rogers wouldn't arouse suspicion, and trusting either of the two was a calculated risk. Assuming that Rogers might object (again warranted), he ordered Natasha to retrieve the data without telling anyone else on the team about her objective. Had this occurred, Natasha would be the only person who knew that Fury had the data, which is something Fury could work with. She did not appear to know the nature of the data, either, which is probably another reason he trusted her with the retrieval mission - she was known for getting the job done without asking questions.
EDIT: I should add that, as events unfolded, Fury obviously decided he could trust Captain America and, by extension, Natasha, with what was really going on.