Is the vacuum in the top of the jar exerting the same force thought the liquid, like the pressure would be if >>>turned right side up<<<?
If so then the small opening between the card and the jars neck would be enough to resist the water flowing from the jar.

One way to test this is...

To make a small hole in the jars bottom and cover it with a finger. Then as the jar and card is rotated card down and stabilized,
Remove the finger from the hole, With predictable results. I think vacuum plays an equal or greater part in the trick.

You're absolutely right. When you turn the jar upside down and the water flows down onto the card, the space left behind has a lower pressure than the outside atmosphere. The difference in pressure means that there will be an upward force on the card and water which opposes the downward weight force (this is the same principle that causes "suction"). While adhesion and cohesion are sufficient to hold up the card when there is little or no water in the jar, for any significant weight of water the difference in pressure is necessary to make the trick work.
Thanks for this important clarification.

A. Weiner