What is happening behind the scenes when one “nurses a grudge?” Is the implication that the grudge might fade or recede without being nursed, actually correct?

We would say it is a faulty assumption, that one can simply stop nursing a grudge and then it might go away or fade in importance. To some extent, "out of sight is out of mind" and this will keep things from getting worse, but when one encounters someone they believe to be a foe again and again, a past grievance can easily become a grudge against that individual if there is no restitution and no way to resolve differing world views where a person is left feeling they have been slighted or harmed in some way, and whoever caused the harm is unwilling to apologize or make restitution. That act of unfairness left unsatisfied can grow into a grudge against that transgressor where the mind will essentially be triggered by their popping up again, and that resentment will bubble up within to make the person unhappy and cause an emotional reaction that might well be in the form of a backlash to inflame the situation further. It is never a good idea to fight fire with fire, and that is the danger in holding a grudge because someone will always be carrying beliefs that will inflame passions and it takes a great deal of restraint to not express this or show it in one way or another in one’s demeanor, if not words, and the other party will pick that up and see they are still being hated and may well dig in their heels and give no satisfaction at all through any act that might ease tensions when that is sorely needed. Acts of loving kindness are the best defense against an attacker, but this is counterintuitive when people feel under threat—to be more loving, to be more giving, more understanding, more tolerant—but that strategy can work when dealing with a normal person; it will not work with a sociopath, but that is a different matter. One must know one’s opponent, and that is an aspect of wisdom as well, to cultivate so one has more than one arrow in their quiver, so to speak, and can deploy the best strategy and, in effect, have a control over the tenor of their response to any given situation in a way that will be productive rather than counterproductive, and will serve the goal of healing the rift, the reason for animosity in the first place, and this will always serve the soul because it will prevent further wounding. So it is better to use diplomacy than to go to war; it is better to make a compromise from a position of inner strength but a willingness to tolerate the foibles of others, seeing they may not be able to help themselves, than to risk one’s life simply because one feels righteous, being in the right, in how they see the situation. This is the wisdom in the saying, "Discretion is the better part of valor;" discretion is a form of wisdom acquired through life experience, experienced best while in divine alignment.