TCAS is completely unreliable in azimuth so your 5 mile estimate is irrelevant to the story.
Completely unreliable in azimuth?
Contrary to your statement,
Faire d'income, I have found TCAS quite reliable, and in agreement with ATC advisories as to position of other traffic, esp. within 20 nm.
Foreign Worker has indicated that the aircraft were on Approach Control, so normal separation standards were apparently in probable contravention of the regulations. It is only on the very rare occasion that controllers on Japan App. allow aircraft to come closer than 10 nm, in my experience.
Additionally, traffic into FUK often enters from the East and West ie. head on, and if this were the case in
F.W.'s example, with 200'-300' vertical separation and a closure rate of say 400 kts, I can understand his/her concern.