Sivaramakrishnan is seen as a lackey for the Board of Control for Cricket in India (BCCI), which doesn't have a players' body and doesn't recognise Fica.
The ICC specifically told its national boards to stay out of the process.
The vote was to be done by the 10 national captains, but it is alleged the BCCI exerted pressure on nations to vote for Sivaramakrishnan.
One captain, South Africa's Graeme Smith, said he was surprised at being asked to vote three times. He stuck with May each time. Others didn't.
This is an issue as much about the ICC sticking to its own processes as it is about May, who is no stranger to butting heads with boards.
The committee already includes another former Indian international, and BCCI commentator, Ravi Shastri.
New Zealand Cricket chief executive David White is the ICC's representative on the cricket committee, which is chaired by former Indian spinner Anil Kumble.
Fica's legal adviser, Ian Smith, said Fica was aware boards were told by the ICC to keep their hands off, but accused some of them of applying "direct pressure on their captains to amend their votes".
Jimmy Adams, former West Indian captain and now Fica president, said the process which removed May had raised significant questions about ICC's ethics.
There is another point worth noting. The cricket committee ranks third below the ICC board and the chief executives' group. It has no decision-making authority, but makes "cricket-related" recommendations to the executive panel.
Two years ago it unanimously recommended the introduction of the Decision Review System for tests and ODIs. A fat lot of good that did.