Hi URSTech,
This is a recommendation for mattresses that have a latex support core because latex is more flexible than polyfoam and can sink into gaps more easily over time. For a mattress that has a polyfoam support core then wider gaps would be fine although more slats and narrower gaps would still provide a more even and supportive surface.
As long as they provided good airflow then it would be fine. For example if you had 1x3 slats that were only an inch apart the airflow would still be fine but if you used 3 sheets of plywood that were divided in thirds (each @ 26" wide) with only an inch in between them then there would be little airflow under the mattress. The amount of flex under the mattress will depend on the design of the foundation and the type of wood (see post #3 here) and the thickness and width of the slats and the less flex the better. There are also some good DIY foundation or platform designs in the foundation post here (under the KD foundation section and the slatted platform bed section) that you can use as a reference.
Phoenix