An invoice has a bank account on it, a supplier's terms, your own address, and what you paid. That is not something to hand to a website and hope. BillSight reads invoices on the machine they are already on.
There is nothing to sign up for and nothing to send. BillSight is a program you install and run; the reading happens in front of you.
It works with the network cable out. That is not a mode you switch on - there is simply no part of it that talks to a server.
The copies it keeps of the originals are ordinary files where you can see them, not rows in somebody's database. Delete the folder and they are gone.
Exports go to the file or folder you pick. Nothing is written to a shared drive, a sync folder or an account unless you choose one.

You still get the rows: vendor, invoice number, dates, currency, subtotal, tax, total due, line items - into Excel or CSV, in the shape your books want. The difference is who ends up holding your suppliers' bank details. See which fields it reads »
Turning a month of invoices into one spreadsheet · Checking whether an invoice has already been paid · Proving what arrived, and that it has not changed
Everything happens on this computer - your invoices are never uploaded.