Not a wrong concept in saving, but their goals are different. There are those who save for the short term, for example saving from spring to meet winter. Some are saving for the long term, for example they are preparing for their old age. It doesn't mean money can't be used, even if there is a emergency need, the savings will definitely be used if the monthly spending money is insufficient.
Whatever the term we choose, short or long term I think a saving will still define as a money that we set a side for a while, in use for later. Our primary goal on why we save is to secure our future so that we will have a peace of mind but life is unpredictable. We are living a healthy life right now but who knows we might experience a sudden pain which can be life threatening if not treated ASAP?
We are now forced to use a portion of our saving to treat it. The same goes if we get into accidents. It's useless if you will save but you won't still use it at the end because you are now gone in this world, unless if the saving is intended to your kids and other family members.