do portable apps REALLY leave nothing behind?

There is always something left behind on a PC when you use any app, installed or portable.

From the page you got that quote the very next point is "A portable app doesn't leave registry entries behind except those automatically generated by Windows" because Windows (and most firewall and antivirus software) record the apps you run in the registry.

Portable apps made to the PortableApps standard always keep your personal settings etc. with the app, but that doesn't stop temp files from the app being left behind, Windows generated files referencing the location or files of the app or any other software like keyloggers from doing what they do.

If you are really that untrusting of a loaner laptop from your repair company why are you even getting it repaired there? If you trust them that little I would be as worried of them putting a keylogger on your laptop before they give it back as much as I would of them loaning you a laptop with a keylogger on it.

EDIT: One way to be security conscious here would be (if your laptop is actually working at this point in time) to go through the Processes tab in Windows Task Manager, record each entry and compare it again after you get it back. Googling any given process name will usually bring up a wealth of information about the safety, validity and/or danger of a process.

If you can boot from either a CD/DVD or from a flash drive, then some sort of live disc of an operating system like linux would be your best bet.
Those are basically operating systems designed to run from read-only media, and will not attempt to write anything onto the computer.
Therefore they are good for security, but would require any configuration to be carried out each and every time.