The organisation is required under its founding legislation to take directions from ministers in the Scottish Executive. Ministers exercised their power recently to force through a head-office move from Edinburgh to Inverness against the wishes of the board.
But according to the Scottish Council for Voluntary Organisations (SCVO), this contradicts charity law, which requires charities to be independent of the state.
The Inland Revenue 'recognises' charities in Scotland using guidance from the Charity Commission for England and Wales. The commission's interpretation of the law states that charities cannot be set up to carry out the "directions of a governmental authority".
The SCVO wants the law changed so that Scottish Natural Heritage along with other non-departmental public bodies also registered as charities, such as the Scottish Arts Council, are subject to a robust test of independence from government.
Stephen Maxwell, SCVO associate director, said: "This case highlights the importance of charities being independent and being seen to be independent from government - central and local - in both constitutional terms and governance practice.
"The SCVO believes the new Scottish charity law should make independence a condition of eligibility for charitable status, with government's power of appointment being limited to a maximum of one-third of trustees."
When contacted by Third Sector, Scottish Natural Heritage initially denied it was a charity. But a spokesman later said: "We have charitable status for VAT purposes but we don't regard ourselves as a charity.
"We save around £650,000 a year through concessions on the rates and VAT, which you could argue is just government money going round in circles.
"We expect to lose our charitable status soon. We don't plan to have it in the future. We applied several years ago and we were deemed to be eligible."
It appears that the Inland Revenue broke charity law in granting Scottish Natural Heritage charitable status, as did the Scottish Executive, in giving directions to the charity.
Maxwell commented: "This just illustrates the absurdities that have accumulated in the absence of explicit criteria on independence. Charity Commission guidance is there but it hasn't been applied, and it needs to be put in statute."