Neil Doncaster and John Nelms could be cross-examined by Hearts and Partick Thistle's legal representative if their battle against relegation is heard in the Court of Session.
The lawyers acting for the Scottish Professional Football League, and promoted clubs Dundee United, Raith Rovers and Cove Rangers, have both called for the dispute to go before an arbitration panel convened by the Scottish Football Association.
But David Thomson QC, acting on behalf of the relegated clubs, claimed the matters were of "significant and legitimate public interest" and should therefore be heard in an open court.
The resolution that ended the season and thus relegated Hearts and Thistle hinged on Dundee, who changed their mind after initially submitting a vote which would have scuppered the plan. The SPFL said Dundee's email had got lost in its quarantine system.
Thomson stated that most of the grounds of the two clubs' complaint were related to documents rather than what anyone saw or heard.
But he added that the "Dundee vote" and the evidence of communications between SPFL chief executive Doncaster and Dundee managing director Nelms were the type of issue which might be subject to evidence and, agreeing with the judge, possibly cross-examination.
Thomson also gave an example of what he branded a "remarkable episode" on June 26 when the SPFL told clubs it was "necessary that they join forces to oppose the petition in order to see the pleadings" following an apparent request from clubs to see court documents.
He added: "That type of episode is a matter of significant concern and legitimate interest which strongly favours hearing the dispute in a public court."
Thomson also claimed there was no valid clause in the SPFL rules that clubs should go to arbitration and, referring to the arbitration clause in the Scottish Football Association articles, argued that his clients had brought the case as SPFL shareholders rather than SFA members.
Garry Borland QC, acting for the three promoted clubs, counter-argued that the SFA article, which states that approval from the governing body's board is needed to start court proceedings, was a precondition of legal action and did not preclude it.
Lord Clark will continue hearing the arguments, as well as Hearts and Partick Thistle's motion for the release of documents, on Friday morning.
