Actually, I think that's not really the case. At least, there are other factors too, which may dominate.
The adhesion is very similar to Wringing of Gauge Blocks. Air pressure does not fully explain the effect, as it can still be observed in a vacuum. It is also believed to be in part due to surface tension in any liquid between the bodies, however the effect is still observable when they are dry. The main mechanism is believed to be something similar to the van der Waals force, although it's still, I believe, not perfectly understood.
I've also wrung gauge blocks together myself. The adhesive force can be quite strong. Apparently, it can be significantly stronger than is explained by air pressure alone.