Well, I can't answer in absolutes, and honestly this isn't my area of expertise (though I did do some employment work during law school), but since most states are at-will employment states, employers in those jurisdictions can fire you for any reason at all, so long as the reason is not shown to be related to the employee's membership in a protected class (age, race, gender, religion, disability, and in some states sexual orientation).
A policy might offer some evidentiary leverage, but I am pretty sure that it does not supercede the "at will" nature of the employment, since technically in an at-will situation you could be completely blameless, and the employer still can arbitrarily fire you. The exception to this rule is the unionized workplace, in which the employer effectively "contracts out" of the at-will arrangement, or an employment contract which binds both parties to a certain period of time.
Regarding protected class membership, employment discrimination cases are litigated in the following way (generally):
Plaintiff alleges discrimination- disparate treatment based on membership in protected class. Plaintiff proves membership in class, and the fact that treatment was disparate. (White/young nurses not fired, nonwhite/older fired)
Defendant has burden to show legitimate, nondiscriminatory reason. (Like insubordination, or absence during snowstorm)
Burden now shifts to plaintiff to show that the reason offered is pretextual, and real motivation for treatment is discriminatory.
In the case of these nurses, hypothetically, let's assume for the moment that there is discrimination alleged, and that all the affected nurses fell into a protected class. The policy could serve as evidence of pretext for discriminatory intent (regardless of union status).
Again, not my area of expertise, and the law varies by jurisdiction, but that is the general idea.