Is $1,900 to survey property lines and place stakes a fair price?

I want to replace my old fence with a new one. I have an arbitrary idea where my property lines are, and town hall provided an old site map that they said is probably not accurate. My property is simple and square. Town hall told me I would need a land surveyor to get accurate property lines. I'm looking to replace a backyard fence, as the side fences are clearly mine. The fence lining the back of the yard has a different style, and I don't know if it's mine. I'm a new homeowner and thought the quotes for land surveying were quite pricey considering the size and simplicity of my lot. The surveyors told me their service primarily involves putting stakes in the ground. I'm confused why the state doesn't know the property lines for sure, but private land surveyors do. I'm also wondering if I can just go off the measurements on the site map from the state, even though they said it might be inaccurate. I'm considering just knocking on my neighbor's door to ask about the fence and then replacing it where the old one was, as I feel nobody would give me a hard time since the current fence looks bad.