The call prior to beginning duty is a courtesy. It isn't reasonable, nor enforceable, to expect employees to know for certain they will be well fourteen hours from now when their window closes...or at any time during that window.
The FAA expressly forbids one to fly if one is not fit to do so. There is nowhere in the regulations that reads "A pilot must self-assess fitness for flight by no later than 6 a.m., and if fit at that point, must complete any flights, planned or unplanned, that are assigned during the following fourteen hours."
Do you seriously think the company is going to be so stupid to take disciplinary action if you call in sick after you perform a personal aircraft evacuation just before handing out the manifest so you could puke in a trashcan on the ramp in view of the passengers? Four hours? Give the company as much heads up as you can, but don't feel bad if you get sick inside of four hours prior to report. God knows they don't give a **** about you and your family.
I think the decision to wait to call in sick until an assignment was given might be a bit of a stretch, though that's certainly no more unethical than contract violations the company commits on a daily basis.
Personally, I would probably have called in sick as soon as I realized I wasn't fit for duty, but I also think it's reasonable if one is borderline fit for duty to take a look at the assignment once it's given and make a decision whether they are able to proceed. There's a big difference between coming in for a DAY out & back, and being fit to accept a four-day trip if one is borderline sick. The last thing I want to do is have a flight I was scheduled to operate cancel at an outstation because I was trying too hard and couldn't continue.
Ultimately, issuing SD's for sick calls is simply pilot pushing. The SD is the only tool a scheduler has to take out their frustration from being put in a no-win situation. If the airline was adequately staffed, and crewmembers were being utilized effectively, pushing crewmembers to operate in a potentially unsafe manner wouldn't be necessary.
Remember, the management philosophy at Delta with regards to Comair is "Take away resources until the operation becomes unsustainable, then give back 1% above that level." They're simply trying to wring every last ounce of effort out of the worker bees in order to increase the amount of honey they can hoard for themselves.