Before 1998, we used to think that the cosmological constant (CC) was zero. Many people were designing explanations why it was exactly zero and supersymmetry was suspected to be the only plausible symmetry that can explain the vanishing result.
Since 1998, we have faced two problems - we not only have to explain why the CC is essentially zero but we must also explain why it's not quite zero but a tiny positive number instead.
One of my favorite verbal solutions of the cosmological constant problem went as follows: de Sitter space has a positive CC, anti de Sitter has a negative CC. Inevitably, de Sitter space annihilates with the anti de Sitter space and the result is a vanishing CC. :-)
The paper by 't Hooft and Nobbenhuis is serious but it shares some of the features with my old joke. They demand unusual complexified invariances of the vacuum state under "x^m goes to i.x^m" as well as "x^m goes to x^m + complex_vector^m" and argue that the only state that can survive this new policy is a state with Lambda=0. The ideology behind this reasoning is that the positivity and reality of observables such as the energy is just a consequence of the boundary conditions at infinity but fundamentally, the equations of motion have a much larger and possibly complexified group of symmetries.