It doesn't need to be larger than 3x3 mm because they rely on in-pad vias to take the heat to other layers. The thermal performance without these in-pad vias would be hopelessly bad whether it was 3x3 or 4x4.
They are talking about solder mask, the green stuff. No, you don't want solder mask over an in-pad via because, as they say, it tends to hold the IC up too high. The industry deals with the problem of solder leaking out those open vias by either plugging them during the pcb fab process (Plugged via or button print via, or plugged and plated-over) or by making them so small that they really don't leak enough to worry about (ie. less than .008 inches dia). They usually don't recommend simply putting solder mask over the via on both sides (so-called Tenting) because during reflow these vias tend to explode in a very tiny way when the internal trapped moisture boils. Its ok to tent the via only on the IC side if you can tolerate the IC sitting high on the pad, such as when doing a prototype. For one-off and prototypes, just letting some solder leak out the other side is tolerable, so no need to do anything but make the in-pad vias narrow.