That his statement - in a widely-trailed speech delivered at Wellington college on Wednesday - grabbed the headlines, and the lead story slot in Sunday's Observer ("Single-sex schools 'no benefit for girls'") - proved the first part of this statement. The second bit, of course, is much more contentious.
The thesis of Professor Smithers, director of Buckingham's centre for education and employment research, is that there is no strong evidence to indicate whether single-sex schools are better or worse.
He attacked two central arguments used by supporters of single-sex schooling. First was the claim that boys and girls do better, academically, if freed from the distractions of the opposite gender.
Professor Smithers presented National Foundation for Educational Research figures for GCSE scores, showing that girls' comprehensives, but not boys', do slightly better than their mixed counterparts. Among grammars, the position was reversed, all boys' schools doing slightly better than co-ed ones, but with no advantage for girls' secondaries. This hardly amounts to proof, he said.
Girls' schools league-table dominance is probably more due to the fact that the top-performers are selective, and cater for middle-class pupils and that girls overall do better than boys.
The second argument is that boys and girls are less likely to opt for "stereotyped" subjects - maths, physics and computing for the boys; English and sociology for the girls - if educated separately.
Yet Professor Smithers unveiled statistics showing how girls' share of A-level physics entries has increased from under 15 per cent in 1960 to 22 per cent last year while the number of girls' schools has slumped.
And girls are only slightly more likely to opt for maths and science at A-level if educated in girls' schools, he said.
There were few defenders of single-sex schools at this week's conference, organised by Anthony Seldon, the new master of Wellington. The Pounds 22,995-a-year school is admitting girls to Year 9 and 10 for the first time this year.
However, Elspeth Insch, head of King Edward VI Handsworth school, Birmingham, said: "We should be offering parents choice and variety, and that's why I believe girls' schools should exist."
Miss Insch said the sciences and maths were the most popular A-subjects at her school, a state girls' grammar. Her experience was that boys would sometimes brand girls "lesbians" for choosing "boys" subjects.
Professor Smithers is not saying that single-sex schools are worse, however - he chose to educate his two daughters at one. He also unveiled figures showing that parents favoured single-sex or co-ed for their children if they had experienced it themselves. And teaching quality was far more important to pupils' achievement than type of school, he said.
For all the controversy, then, the debate seems to boil down to this: parents should choose the school that works for their children.