In the PAC-learning setting, it is easy to learn a CNF formula when we know each clause has at most $c$ variables.
We go through each positive sample, and eliminate every clause that contradicts the sample.
Learning a DNF formula is said to be much harder, but it seems a similar procedure can be used, so it is unclear to me why DNF is more difficult.
Start with all conjuctive clauses that have at most $c$ variables. Go through each negative sample, and eliminate clauses that contradict the sample.