From [10.5.2], "Then the attacker, followed by the defender, may each play one Event card that is used during a battle, before the die is rolled."
Do the Play Anytime 'Cancel the just-played card' events count for this?
No they do not, you can play them "anytime".
Don't forget rule 5.3.2:
[5.3.2] Event Precedence: When there is a conflict between Event text and the Rules, the Event text takes precedence.