No, there's no sense in which the Treasury Board would supervise the work of the commissioner. The role played by the Treasury Board Secretariat would be to support the president in any amendments that were made by the government to the legislation.
Mr. Saxton spoke about changes that were initially made by the government in 2006, when the Lobbying Act itself was introduced, and it came into force in 2008. On the subsequent amendments that took place in 2010, the content of those would have been prepared by officials within the Treasury Board Secretariat and supporting the minister responsible for that legislation who introduced them to the House. But it's not a supervisory role over the commissioner.