But, the second most popular option was to pay via credit card, and this does not preclude having the money in savings. Given the popularity of credit cards in the US, this makes sense too. If faced with a sudden large expense, I too would put it on credit and pay it off at the end of the cycle instead of pulling from savings, despite being able to afford the latter.
Similarly, the third most popular option was to pay the bill and cut other expenses, which also doesn't exclude savings and would be a pretty normal thing to do too.
IIRC only ~15% said they'd take a loan or borrow from friends/family.