Primaries four to seven returned to school on Monday, along with part-time lessons for secondary schools.
The decision was originally announced by Nicola Sturgeon on March 2 – the day before she appeared before the inquiry investigating the handling of harassment complaints against former first minister Alex Salmond.
On BBC Scotland's Sunday Show, Andrea Bradley, the assistant secretary of the EIS teaching union, said the Scottish Government was looking for a "good news story that week".
However, Ms Sturgeon had previously announced the earliest date for some pupils to return to school would be March 15.
On Monday, education secretary John Swinney rejected the claim.
"There is precisely no connection between those two events," he told Good Morning Scotland.
"The government previously indicated that we would provide an update on the return to schooling on that particular Tuesday.
"That is precisely what we did and we addressed the concerns about the wellbeing of children and young people in driving the decisions that we arrived at."
Ms Sturgeon had previously criticised the decision of the UK Government to allow all children in England back to school on March 8, claiming it would send cases "through the roof".
However, the education secretary denied the return on Monday amounted to the same approach, just delayed by a week.
"Pupils in England returned full time in all areas on March 8 – what we're doing is we've taken a staggered approach to that over a longer period of time," he said.
"We're taking a measured approach, commensurate with the advice that we've got, which enables us to do two things.
"It enables us to address the wellbeing concerns that many people have about our young people who have suffered during the lockdown and the pandemic, and it also enables us to sustain the delivery of education for children and young people within Scotland."
With the return of schools increasing, Mr Swinney said there would be outbreaks within schools, but claimed this would be driven by the prevalence of the virus in the community.