Is AUTHOR wrong in the post ? POST : Please read this because I know the title is wild and seems clickbaity but idk how else to shortly describe the situation? 

Monday driving home from work on a country road just a mile from home, a dog suddenly popped out of a cornfield a few feet from the road chasing something and I hit it. I tried so hard to break, but he was just too close. I got out of my car, saw his neck was quite obviously broken and I *abso-fucking-lutely* bawled my eyes out. I sat in the road for five minutes holding him and sobbing, I felt so fucking horrible. I have three dogs at home so my heart was just aching with guilt. My car is fucked, the bumper was ripped off and had some leak and I'm dealing with an insurance claim now over it..

The dog had a collar with a number so I called it. The woman answered and started crying. She came to get the dog and brought her 3 kids.. idk why.. and they were all just bawling. I felt so fucking bad, I hugged them all, apologized, explained what happened, and told them he died instantly so there was no pain and he just went to doggy heaven peacefully. 

I had an emergency blanket in my car so I wrapped him up in it and she took the dog home. My fiancé picked me up and my car was towed away. 

Anyways, today I get a text from her (she must've had it from her call history) requesting that I pay to cremate the family dog because I'm the one who killed him. Well, not just cremation, they want a paw print memorial stone and a little vase for his ashes and it's all going to be a total of $150. 

I haven't responded to the text. Now, honestly, normally I would as I want to show I truly regret it and am sorry because I can't even imagine my dog dying. 

But for one, I know for a FACT I've seen the dog roaming around before as the dog had very unique markings and was a more rare breed.. so I assume he's let loose frequently. Two, I'm dealing with my car insurance claim and my deductible is nearly $1k so I'm about to be in big trouble financially as it is. Three, I'm a BROKE ass college student and I live literally paycheck to paycheck. And four, it was truly an accident and there was NO way to prevent it other than the dog not being there. 

I'm really in a rut here. I have so much guilt, yet I feel like even though I did do it, it wasn't really my fault...

WIBTA if I said no to paying them for this? 

TL;DR: Accidentally killed dog while driving and also badly damaged my car. Dog's family wants me to pay for cremation and optional memorial items. I am extremely broke already. I am conflicted. 