I think your article actually proves that time off can be taken in this case - relevant quotes below from the article linked:
So time off can be taken for:
To deal with the unexpected disruption, termination or breakdown in care of your dependant (for example, if your childminder fails to turn up)
Such as an unexpected disruption to the childcare arrangements
Things to consider:
Is there anybody else that can help?
Is there any other arrangement that is possible?
The OP and her DH have considered this and found another childcare solution, but had they not been able to find anyone else they have at least covered this off
Unplanned doesn't have to mean that you haven't had warning:
However, knowing in advance that something will happen does not mean that you definitely cannot take time off, so long as the time off is necessary. In the case of Royal Bank of Scotland plc v Harrison the Employment Appeal Tribunal found that a mother who had two weeks’ notice that her childminder would not be available, and who had tried but was unable to make alternative arrangements for her children, had taken time off for dependants when she was absent from work.