As far as I understand, yes she will need to self-quarantine with no public transport for 14days, domestic transit is considered public transport (that’s what ANA website says), rules are the same at NRT and KIX, she still has to quarantine even after negative result.
Reguilar taxis are considered public transport, but I wasn’t aware of “Covid friendly taxis.” Best option for Jpn nationals returning from USA and Europe is to get picked up by family even if it involves a long drive, although I know that’s not feasible for some. Good luck!
Eta:
official info in Japanese
https://www.mhlw.go.jp/content/10900000/000618977.pdf