I always accepted my x's offers to take the kids, unless it was impossible for me to do so (i.e., work travel).
But if she ever asked for comp time, it was always at my discretion, not hers. I never chose to be a jerk about it, despite her regularly scheduling events on my parenting time. Whenever I was made aware of this, I just advised her the kids wouldn't be there, unless of course she preferred to switch, and I always got the comp time before her switch days.
Sick time is different, though. If i was ever sick, that meant I was unavailable for parenting, so I lost out. Same thing for work travel. I was lucky to be able to plan my travel for my non-parenting time, though, for the most part.
A rule of thumb is, switch when there is something cool or important for the child to do (providing your comp time happens first). If either parent is unable to meet the responsibility of their parenting time, however, they lose that time, unless the other person feels gracious.
"Personal density is directly proportional to temporal bandwidth."