Hi bkim,
The wider spacing is probably because they are using 1x2 slats instead of 1x3 and this is too far apart for a latex core mattress IMO.
There are different types of bunkie (bunky) boards and the same guidelines would apply as for a foundation or a platform bed surface. If the spacing in any gaps is less than 3" (for a latex core mattress or slightly wider for other types of foam support cores) and the construction is strong enough for the intended use it will have … then they would be fine. Some examples and sources for bunkie boards are in post #4 here. I would tend to choose a platform bed where the slats were already appropriate however unless I really wanted a specific platform bed which needed better support than the slats provided and a good bunkie board was necessary in order to make the bed suitable for my mattress.
The wider spacing may work for a polyfoam support core (polyfoam is less flexible than latex) but if there is any doubt about how suitable any type of base would be then I would always check with the manufacturer of the mattress.
Since the advantage of having slats (or a grid) vs a solid surface is greater ventilation (which allows for better control of humidity in the mattress and reduces the risk of dust mites, mold, and mildew) … I would tend towards a closely spaced slatted surface in a bunkie board (instead of a solid sheet of plywood, particle board, or cardboard on the surface) with a good quality fabric on top and would make sure the construction and materials were strong enough for the combined weight of the mattress and the people on it. Some bunkie boards are designed for the use of children or very light people in a bunk bed and would not be an appropriate choice. There is more about a solid surface vs a slatted surface in a support surface for a mattress (platform bed or foundation) in post #10 here.
The other advantage of a suitable and well made bunkie board is that it can provide a suitable surface for a mattress without adding the height of a standard or even a low profile regular foundation. I would personally choose a slatted surface though regardless of whether a mattress was being used directly on a platform bed, a foundation, or a bunkie board unless there was a compelling reason to use a solid surface (such as someone who wanted an adjustable bed in which case a solid surface may be the only option).
Phoenix