The old phrase "They are called Minutes and not Hours" is applicable here and if the Clerk undertook CiLCA training then they would cover this in their studies. Minutes are a record of decisions made and not discussions and the action of the Clerk to note everything said by every Councillor could lead the Council into possible legal issues.
If the Clerk is so concerned about having everything minuted, then they could record the meeting and keep the recording on file and keep the minutes as brief as possible. That said, there would have to be a statement read out at the start of the meeting, that recording is taking place etc.etc.
The difficulty is that the Clerk is responsible for taking the minutes and therefore it is their personal recording of the meeting that the Councillors approve at the following meeting. However, the Clerk is an employee and therefore could be instructed to amend their practice, and be offered training via the Local Council Association - after all it surely takes more time to do a verbatim report than proper minutes? As a final resort, the Parish Council could refuse to approve the minutes but only if they were factually inaccurate - but this could make a point....