Yes indeed he could and probably would. WAS's, and in particular men going through MLC, can be very sneaky. They will say things like that because they want YOU to tell THEM when YOU meet someone. They on the other hand want to keep what they are doing completely secret.
No doubt that he wants to keep it a secret. Affairs thrive in secret! Once the affair is known the fun of it starts to go away and shame comes out.
Here's to hoping the affair comes to light soon. It's his mess to clean up, not mine.
BTW going out with friends this weekend. By myself!