Others have already explained that an anti-pad is a copper keepout area surrounding a structure, usually a via but it could also be a via. The intention is to increase the copper to copper clearance on the layer of choice.
However, I don't think anyone has answered your high frequency question regarding skin effect of return currents. I agree that the return current path is critical. Usually we would like the most direct path between the signal source and sink. However, in practice, the return current path will the the path of least impedance. In practice for electromagnetic reasons not explained here, this is usually in parallel to the signal's current path. That is the return path doesn't usually obey Pythagorean theorem.
This is where via stitching comes in. As you said, the return current must get from the top of the plane to the bottom. The best way to do that is to place a parallel via for ground right next to the signal via. We could even put multiple vias to reduce the via's impedance to the return current path. Ultimately, we want to reduce the distance/impedance the return current needs to find it's way back home.
Here's an example 10129181 Amphenol FCI of a 25 gigabit Ethernet backplane connector. Notice the recommended layout. There are pairs of signals for each Ethernet lane. Next to every signal via is another via. This is for ground. This reduces the return current path distance and also has some EMI/crosstalk shielding benefits. This is much better than having the ground signals bunched up together.
Here's an example 09062216883 Harting of a connector that a schematic designer could mess up. This connector offers beautiful power pins. However, if the designer doesn't allocate stitching ground pins on the signal side, the return current path will be forced to travel extra distance through one of the 5 power connectors.
There are more differences between these two connectors that make them suited for different signals but I only hope to answer it as it relates to return current paths.