I think the consent is less about what the ambulance/doctor/hospital can do, and more about whether the childcare centre is allowed to initiate the seeking of the ambulance/doctor/hospital on behalf of the child's parent/guardian in your absence.

I for one have had the occasional situation where the carer/school were not able to contact me immediately, (but thankfully never any dire emergency). I would not want the centre to be waiting until they have spoken to me to decide to call an ambulance if an ambulance was needed straight away. I sign the consent.