The PMW says in a footnote:

In this document when we speak of the private or unofficial use of the keys we mean the duty and authority belonging to individual believers (the Universal Priesthood of All Believers) which is their personal responsibility toward their neighbor. When we speak of the public or official use of the keys we are referring to the duty and authority of those who are called to act on behalf of Christ and His believers.

In this way, PMW makes "public" and "official" into synonyms, and it makes "private" and "unofficial" into synonyms. The first two mean "belonging to those called to act on behalf of Christ and His believers." The latter two mean "belonging to individual believers." Thus, "private" is used according to the customary meaning of "unofficial," while "public" is used according to the customary meaning of "official." This leads to some confusion in the first section of the PMW, on the Office of the Keys.

There, the PMW says:

The church uses the keys to preach the Gospel, administer the sacraments, and practice church discipline. The keys are used privately or unofficially when individual Christians, on behalf of Christ, speak the Gospel of forgiveness to others; when they forgive the sins of those who sin against them; when they retain the sins of those who do not repent, e.g., when they confront in a brotherly way those who need to repent of their sins; and when in "the mutual conversation and consolation of the brethren" they comfort one another with the words of the Gospel.

Most of this quote describes the "private" or "unofficial" use of the keys, under the heading "The Office of the Keys." Do you see the confusion? If the PMW means to describe "The Office of the Keys," why does it instead describe the use of the keys without the authority of any office? That is not the office of the keys, by the PMW's own definition.

There may be reasons to describe the unofficial use of the Keys in the PMW, but it should be clear that it does not fall under the heading "the Office of the Keys."

It may be ideal to place the unofficial use of the Keys under its own heading, to separate it from the Office of the Keys, where it is currently found. However, I realize that the ELS is a conservative synod, and is therefore resistant to changes --- even good changes. So my recommendation is to change as little as necessary to remove the confusion.

I recommend addressing the Office of the Keys explicitly from the start, and then moving on to describe by example the unofficial use of the keys by individual Christians. That way, "office" and "unofficial" will not be confused with each other.

Here is suggested wording to replace the current wording I quoted above:

The Office of the Keys is the church's authority to preach the Gospel, administer the Sacraments, and practice church discipline.

Individual Christians also speak the Gospel of forgiveness to others, forgive the sins of those who sin against them, confront in a brotherly way those who need to repent of their sins, and in "the mutual conversation and consolation of the brethren" comfort one another with the words of the Gospel. This may be called the private or unofficial use of the keys.

There is another advantage to this wording. It eliminates another slight redundancy that is bound to cause confusion. The PMW currently reads "when they retain the sins of those who do not repent, e.g., when they confront in a brotherly way those who need to repent of their sins." While the example helps to clarify what sort of "retaining" is meant, the common understanding of retaining sins can refer to each step in Matthew 18:15--17. Since the PMW does not mean the last step, it is more suitable to use the example given in the PMW by itself. That eliminates the redundancy, and makes the intent of the PMW clearer.

Once you've digested this, feel free to tell me exactly where I'm wrong. That's the sort of thing the Plucked Chicken is for.