YANBU. I don't think enough people talk about how expensive it is owning a pet, and people get them without thinking about just how expensive it can get, especially when things go wrong. At the very least, if you don't have access to relatively large amounts of money, the pet should be insured. I hope the woman you mentioned finds a way of treating her puppy though :(
I have a mutt, so that in itself means she's unlikely to develop any pre-existing conditions in any one breed. I didn't insure her for this reason as well as being skeptical about pet insurance. I reconsidered this one-my parent's house is on a hill and backs onto another house, over a small fence but via a huge drop. One day I was playing ball with her in the garden and it went into the neighbour's garden and my heart stopped. Luckily she didn't jump over the fence but she could have done, perhaps really hurting herself-and I rang around insurance companies to make enquiries. None of them would insure for accidents. Their attitude was that if an accident like that happens and she needed treatment, It's my fault so they wouldn't pay out. Fair enough you may think, but accidents happen to the best of us.
So my dog still isn't insured, unlikely to need treatment for illness and insurers won't pay out for accidents HOWEVER I have savings and credit cards with huge limits -if something did go wrong I could afford it to sort it and I would. I've thought it through, many don't.
My skepticism about insurance is borne from other people's experiences, I know a fair few people whose pets have needed treatment and insurers have 'smallprint' which means they've refused to pay out. My friend fought tooth and nail about hip dysplasia when it happened to her dog, insurers stating they'd not pay at first (I can't remember the ins and outs of why). A family member's dog developed a gum condition and the insurance didn't cover it.
Some people seem to factor in costs of food and upkeep and care but not think about illness and accidents. Vets deserve to be paid fairly. I hear of too many stories like this when people just don't have the money and haven't considered that they might need plans for circumstantial change when it comes to pets.