Fiona Hyslop, the party's education spokesperson, brought up the case of Rory Blackhall, the murdered Livingston schoolboy, when school transportation was debated at last week's meeting of the Scottish Parliament's education committee.
Ms Hyslop said members had already expressed their disappointment with the Scottish Executive's revised guidance on school transport. While it addressed safety aspects, the guidance was still very much driven by the legal requirement on parents to have their child educated and by distance rules to qualify for free travel.
She recalled that one of the instigating factors for revised guidance was a petition raised by one of her Lothian constituents and his concerns about the safety of pupils in Livingston.
While there were particular issues about the Rory Blackhall case, Ms Hyslop said, pupil safety generally was now paramount as was the legal responsibility of parents taking their child to school.
She said: "We do not want to have a situation where we are wrapping our children in cotton wool. We do want them to walk to school from a health aspect particularly, but also from a transport aspect because we know the school run is causing a great deal of congestion."
Issues included the responsibility of parents ending when the school started at 9am, working parents having to drop their children off at school and the problem of start dates and times that did not necessarily fit with the working life of parents.
Ms Hyslop acknowledged that the way school attendance was monitored was being examined following the Rory Blackhall case. She urged Mr Peacock to use this opportunity to examine all the issues relating to child protection and transport and reflect on the need for a "joined-up" approach.
This was not necessarily covered by circulars and guidance, which were just about the legal responsibility of parents getting their child to school, Ms Hyslop suggested. "It is wider and deeper than that and it would be useful in Scotland to engage in a realistic debate as to how we tackle risk and the protection of children in a way that helps health, transport and the environment."
Mr Peacock confirmed that the Executive was looking at all aspects of the Rory Blackhall case and attendance reporting. It was also examining the recent case in Edinburgh where a three-year-old boy was trapped in a flat while his mother lay dead.
He told Ms Hyslop it was important to recognise there was a clear legal responsibility on the part of parents. If the state took over responsibility for getting children to school, there would be all sorts of implications.
Mr Peacock stressed that all aspects of school transport were under investigation, including environmental matters. In cases where there might be a potential risk to children in particular circumstances, it was entirely within the discretion of local authorities to provide transport.
Rosemary Byrne, Scottish Socialist Party, said safety should be the main criterion, rather than rules that were governed by distance. She urged Mr Peacock to call on local authorities to give priority to safety "rather than this thing of measuring two miles or three miles or whatever".
Ms Byrne also stressed the need to have "a concrete policy" to ensure greater supervision on school buses, saying its absence left children highly vulnerable.