I think Caemlyn being attacked is a very dire situation.

1. It is a major city with tens of thousands of innocents likely to be killed or worse in the event of a sack.

2. A bunch of important people, both to Rand and the light side as a whole, are residing in Caemlyn and under threat.

3. Having a sizable army of shadowspawn running around the middle of the continent is a huge military blow, requiring a sizable army to be pulled from the borderlands to take care of them, further thinning the lines. Especially with an open waygate and easy opportunity for trolloc reinforcement.

Should we assume Verin thought the army, if Mat didn't open the letter, would be a relatively minor annoyance an able to be taken care of without too much loss?
Or should we assume Verin acted out of character by putting all her eggs in one basket?

She was able to skate her oaths enough to leave one letter, and we saw that she had others, and to give away all the BA she knew of. I think she could have had a back up plan.