The statement in the video is wrong.
Lets assume we can apply a force to the electrons in the wire, in direction to the place.
As particles, they will be accelerated and Start moving to the plate. This leads to a growing overall negative charge of the plate. This charge will build up a force on the electrons in the opposite direction. Only if this force equals the "inwards pushing" force, then no more new electrons will enter the plate.
Depending on the external force and the capacitor geometry, the amount of pushable charge will vary but always be greater than zero, regardless of the sourroundings. There are for example formulas to calculate the capacity of a single sphere in empty space.
To actually apply the force, one can use external electric fields from an electric source or a statically charged object.
The attracting force of the positive charge in the other plate does however illustrate why capacitors with closer plates have higher capacity.