Ms Smith made the headlines with her announcement last week that independent appeal panels would be told not to reinstate pupils excluded by headteachers for extreme behaviour. "If headteachers have to exclude violent or very disruptive pupils then they will have our full support," she told the Professional Association of Teachers' conference.
But it is governors, not heads, who legally must decide whether exclusions should be upheld or rescinded. Dissatisfied parents can then take their child's case to an independent appeals panel.
Chris Gale, chairwoman of the National Governors' Coucil, said she was "irritated" by the comments. "Headteachers do not have the last word. Governors have to uphold their decisions. I'm fed up with ministers undervaluing governors."
Meanwhile, heads warn that the victims of bullies could claim damages against schools if their attackers are not excluded, or are reinstated on appeal.
The new Human Rights Act, which takes effect in October, says no one should have to suffer "degrading treatment" which could include persistent bullying, sexual and racial harassment.
New guidance from the Nat-ional Association of Head Teachers says heads will have a duty to prevent a violation of human rights. David Hart, general secretary, believes damages could exceed pound;1 million in the first year.