One thing they always over look was the fact that back then they had some basic type of radar and magnetic based proximity sensing systems. An actual trick to make a ship "invisable" was to basicaly run a giant degaussing coil around the ship.
This would temporarily make the magnetic based proximity devices on mines and other trap type weapons usless. They were then "Invisable" to the Sensors.
The short term high energy output of one of those big degaussing coils was suposedly able to scramble the basic radar signal so that the enemy radar would not get a usefull return reflection. The actual ship would look so big and distorted that they would asume it was a radar glitch and not a real object.
As far as messing up people, the real facts are that being exposed to very high strength fluctuating magnetic fields can tempoarily mess a persons cognitive processes up.
It can cause some to halucinate or cause upset stomachs and disorientation and confusion.
Throw some good miss information sent out to the enemy and give it a few years and guess what you have, An invisable ship! Add some reports from low raking officers that were part of the degaussing but did not know what was going on or what the effects on them could be and the story just gets built on from there!