With all due respect, if you have to hide something from your spouse because it might upset them...you have to ask yourself, is what I am doing worth risking my marriage? If it upsets my spouse, do I NEED to do it?
Unless your spouse is a control freak who wants to manipulate your every move, then the answer should be no. And if your spouse is a control freak puppet master, you have bigger issues on your hands.
How to destroy a marriage in ONE EASY LESSON -- be duplicitous and sneak around behind your spouse's back in order to talk to an ex. If it is worth sneaking around, he needs to be asking himself why is he prioritizing talking to his ex so highly? I think most people (again, talking about reasonable people, not control freaks) only start 'snooping' when their suspicions have been aroused. Until then, we are just as trustful as the people on here in solid marriages.
If it is innocent, there is no reason to hide it. If it is not innocent, she can't assume he will tell the truth because she asks. If it is not innocent, he is no longer acting as her partner. Regular rules of communication will not apply.

Hopefully he was just being stupid.