The arbitrator in the Kovalchuk case, whenever he or she is appointed (could in theory be up to 120 days from now), will have wide discretionary powers in handling the case and making a ruling.
Under Section 26.13(b) of the CBA, the arbitrator has the authority to force “the attendance of witnesses and the production of documents”.
This means that the arbitrator can require the production of things like emails, faxes and telephone records.
On top of that, as per Section 48.5(d), the arbitrator may find that a circumvention has occurred “based on direct or circumstantial evidence”. Circumstantial evidence casts a pretty wide net. It's evidence that calls on the arbitrator to make a deduction to conclude that a fact exists, such as the parties intended to circumvent the CBA by adding a bunch of throwaway years at the end of the contract. In contrast, direct evidence supports the truth of an assertion directly.
The arbitrator could therefore require the Los Angeles Kings to appear and produce documents since they were involved in contract negotiations with Kovalchuk and may have something relevant to contribute. If it’s indeed accurate that the New York Islanders were involved in the Kovalchuk sweepstakes, they could also be called or asked to produce relevant documents.
In case you’re wondering, it’s not open to the arbitrator to call LeBron James as a witness and demand that he explain why he chose the phrase “I'm going to take my talents to South Beach” rather than just say, "I'm going to the Heat". I wouldn't mind the explanation though.