I think it is important to explain to you why HO6 insurance is important to you, as the owner of this condo. This insurance protects your investment, inside the walls of your condo. The insurance your HOA carries protects your condo outside the walls.
Let's say you go away for a weekend and you decide to run your dishwasher so you have clean dishes when you return, and while you are gone, a water pipe bursts and water is running all weekend. Your HO6 insurance will cover all that damage to your dishwasher, floors, carpet, cabinets, etc. And typically, depending on the price of your condo, this insurance only runs you about $200 - $300 a year! What a deal!
Lenders did not used to require this type of insurance, which is why you were able to purchase your condo without it. But lenders want to protect their collateral, inside and out. Significant damage can happen inside your home. What if you have a kitchen fire? Your HO6 insurance will cover it.
This is a great value, and lenders should have been requiring it all along. As for what happens if you do not buy it? You more than likely will not be able to complete your refi.