The row broke out after figures obtained by Michael Russell, the SNP's education spokesman, showed that HMI is failing to inspect a substantial number of schools within the promised seven-year cycle.
A total of 1,170 out of around 2,650 schools fall into this category. Many primaries have not seen an inspector for 10 years. In Glasgow, 29 primaries have not been paid a visit in more than 20 years.
Mr Russell then declared that there was clearly something amiss. "I think it would be difficult for ministers to talk definitively about the system when there are so many gaps in their knowledge," he said this week.
North Lanarkshire tops the "not inspected" list at 111 schools out of 156.
However, Michael O'Neill, its education director, hit back at suggestions the inspectors and the authority were not doing their jobs.
The figures may be accurate, Mr O'Neill said, but the inference was that if schools were not inspected there was a problem. Not so.
"We have our own framework. We do target-setting, verification and standards and quality reports on a 10 per cent sample. We are well able to identify schools that are struggling and put in support," Mr O'Neill said.
"It is not only HMI that is looking at quality and inspections do not tell us anything we do not know."
Where inspections had been carried out in North Lanarkshire, schools were invariably rated as good or very good.
Mr O'Neill pointed out that HMI is already looking at proportionate inspections and will not focus on authorities which have sound quality assurance frameworks or schools which have good records. In time, authorities would also be carrying out their own inspections, a point underlined by Graham Donaldson, senior chief inspector, in his address to education directors last year.
In a parliamentary answer, Mr Donaldson said that HMI had increased the number of inspections from 152 in 1996-97 to 299 in 2002-03. It is aiming to inspect all primaries by 2009 and all secondaries by 2008.