No, you're not being gullible - I know of plenty of people who could easily have spent that much. What I would question is whether you NEED to spend that much. For a start, if you are fortunate enough to not have any fertility problems, then you only need to buy a couple of pg tests (i.e. that's 300 quid in the story's budget that you won't be spending).
Then there's the nursery - why it would cost over three grand to deck out the nursery, I have no idea. Ours has cost probably thirty quid so far - we have used shelves and a chest of drawers that weren't needed elsewhere in the house, and the paint was left over from decorating our own bedroom. The curtains are the ones that the previous owner left behind - they are now washed and looking lovely, as though they're about a day old. The cot we will buy second hand - our local paper has them for less than fifty quid nearly every week.
If you BF, there's no money to be spent on formula.
If you use washable nappies, you save a lot of money (plus you can use them on the next baby, if you have another one).
Etc. etc.
My point is, it can cost what you want it to cost. If you think a little bit laterally and start planning early, you can save no end of money. Don't ever turn down the offer of something from another parent (you can always give it back later and say it wasn't quite what you needed), go to carboot sales, look in the local paper, and use eBay.
Above all, by reusing stuff, you're not only saving loads of money but also helping to save the planet.