If there is a touchier subject in the workplace than "fairness" I've never seen it. I'm not talking about "our" workplace necessarily: I'm talking about "any" workplace. For positive morale the workplace needs to have an overall sense of fairness; that the rules are known and people are held consistently accountable to them in terms of outcomes and consequences.
The problem with managing an overall sense of fairness is that often people equate fair with equal, and they are not the same thing. Every person is different and every situation is different if only in nuance. Sometimes the most common offenders in mistaking equal for fair are HR people. After all, the laws governing employment practices require that we treat every similarly situated individual in a similar way. While the law doesn't say that, it does in practice. If you treat two similarly situated individuals differently, and those individuals happen to differ by race, gender, age, etc... (as they naturally do in a diverse workforce), you leave the company open to charges of discriminatory employment practices.
Also, a workplace without considerable consistency leaves management opent to accusations of favoritism. Two people do the same thing and get different outcomes and people want to know why. Also your least loyal or charitable employees often jump instantly to the conclusion of favoritism because they don't have all the facts or just because they do that as a matter of habit.
The delicate balance for HR departments is to see each situation in all its complexity and to make good decisions and recommendations on when to depart from policy. A good example would be when somone reports to work after consuming alcohol. When confronted, one employee denies drinking while the other asks for help with their alcoholism. An unsophisticed HR department will recommend termination for both because they committed the same offense. After all, "fair is fair", right?
Well, no. That's an equal approach, but not fair. The more nuanced recommendation is that one person was deceptive while the other was forthright and asked for help. The "fair" result is to termiate one and put the other into required rehabilitation and on a final written warning. The message to the workforce, as the facts leak out over time (and they always do, usually from the employees themselves), is that management cares about their people.
And that, HR practitioners, is the right approach. Do what's right for your people, see past equal treatment to what is truly fair, and see the workforce's trust in you grow over time.