Interview Travel Expenses, Who Pays?

I was asked for an onsite interview (already passed two rounds), but they want me to advance the travel expenses (Flight + hotel, it's about $1K). There is a staffing agency in the middle and I don't trust them. I talked to the agency about this making me uncomfortable, and they still want me to book it. In the past, companies always took care of the logistics. I'm worried that they could decide to ghost me and leave me with the bill.

I'm thinking about declining because of that. Thoughts?