SELECT HOME WARRANTY Told me to wait for approval for furnace that needed replacement when it was 15 degrees outside. Mahwah New Jersey

I reported my furnace not working and the next day a serviceman came that select sent. He said the furnace needed to be replaced and Select said that I needed to wait for approval. It was nearing the weekend and freezing temperatures were coming that night. It needed to be installed before the weekend and I didn't have time to wait for the approval since my pipes would freeze and there are toddlers in the house. So, I paid for the replacement and told Select the situation.  The claims representative said he "understands", but that the part broken isn't covered. Shocker.

In fine print somewhere, the heat exchange isn't covered. The part that most furnaces will need to be replaced for. I don't know why HVAC system is said to be covered? It should say that it is SELECT coverage. Because now I have been paying for a warranty to protect me from this exact situation and it is a sham. I am now paying $3000 for a furnace and SELECT has paid nothing. 

My question is- what was I supposed to do? Allow my pipes to freeze and the small children? So, save your money for your furnace and don't give it to SELECT.