Just to share the other side of the argument - we’ve done many orders for $1,000+ here on Fiverr. Last month we did a job for around $2,500 in a single order, this month we expect to have another, and this is with a brand new seller, with no track history on the platform.
I think you have to apply some of your own business intelligence (what’s your communication with the buyer like? Any red flags?). But also, at some point, you have to put some faith in both people, and the system that’s there to protect you. Outside of Fiverr, you’d invoice. What’s to stop a buyer from not paying your invoice? Sure, you’ve got legal recourse, but what if the buyer goes bust before they can pay your bill? You take them to court, win, and still don’t get paid a penny. I’d argue that Fiverr offers more protection in some ways, due to the escrow system.
It’s your call, because it’s your time on the line. But Fiverr do provide protection to sellers, regardless of what many think. Like @wolfhowler has said, document everything. Protect yourself as though you’re going to get scammed - you hopefully won’t need it, but it’s not the end of the road if something bad happens.