Page 31 last paragraph of the main rulebook says:
Typically, a model can only fire a single shooting weapon in the same phase, although some models, such as vehicles or monstrous creatures, can shoot two or more. Once a Model has fired its maximum number of weapons, it cannot fire again that phase.
What is interesting is that here it doesn't say shooting phase, but rather same phase. This is setting precedent for who can shoot, and how many weapons they can each fire in the same phase.
Page 45 third paragraph.
An Overwatch attack is resolved like a normal shooting attack (albeit one resolved in the enemy's Assault Phase) and uses all the normal rules for range, line of sight, cover and so on. Unlike a normal shooting attack, Overwatch cannot cause Morale checks or Pinning tests. Any shots fired as Overwatch can only be fired as Snap Shots (pg32). Therefore, weapons and models that cannot fire Snap Shots cannot fire Overwatch.
So it is a normal shooting attack, just one that happens to be in the opponents assault phase. Note that we have already established by the rules that Monstrous Creatures can fire more than one weapon in each phase. This is what is normal for them, and later on the rules even say word for word that firing two weapons is the norm for them.
Page 68 First paragraph.
Flying Monstrous Creatures are Monstrous Creatures that have a number of additional rules.
So Flying Monstrous Creatures are Monstrous Creatures, with a few extra rules.
Page 68 third paragraph.
In addition to the special rules that all Monstrous Creatures have, Flying Monstrous Creatures have the Jink and Vector Strike special rule.
So they have all the special rules as they are Monstrous Creatures.
Page 69 third paragraph.
Flying Monstrous Creatures are quick-witted predators, able to track their targets even when moving at high speeds. They can, therefore fire upto two of their weapons normally, even if Swooping (provided that they don't run). Flying Monstrous Creatures can shoot all around, just like other non-vehicle models.
Here it says that Flying Monstrous Creatures, which are Monstrous Creatures can fire upto two weapons normally, note it doesn't say phase or or even mention phase in the paragraph. When they fire their norm is to fire upto two weapons.
From all of this it is quite clear that the intention of the rules for Monstrous Creatures is to be able to fire both their weapons in Overwatch.
The way GW have written that one line is badly written, but this is GW. They aren't the best at writing clear rules, so it is always best to read around a rule, see what else the book has to say before making a rash call. Making a ruling based upon one sentence is ill advised, especially as when shown above there are several clear contradictions to the ruling people are trying to argue for. It is always best to look at the context of what a rule is saying, rather than a breakdown of word by word.