The response as part of 62.6 should be clear and followed. If as it sounds the quotation was not accepted there should have been the statement that the Project Manager will assess themselves or the Contractor was requested to re-quote. Which ever response was the one given should be followed, 13.4 does not now over rule that.
The Contractor would be pretty stupid not to give you the information you need quickly, or you will implement the event based on the information you know, which will be lower than they want in terms of cost I suspect. If it ever went to adjudication the adjudicator would have little sympathy for a Contractor who was not forthcoming with the information on which to make the assessment. You have three weeks to make your assessment, and then even a further two weeks after that before it becomes deemed accepted (if the Contractor reminds you that you have not done your assessment) so by default you have longer really).