The difference is that the "binding" done at the congregational level is of necessity. Someone has to decide what time to meet and the order of worship. Otherwise everyone does their own thing and there is no true corporate worship. This necessity does not exist between two congregations or even two services. If a congregation wanted to sing Psalm 51 to one setting one week there is no necessity that the next time it sings it it is to the same setting.
For a national church to insist on uniformity in the use of a certain psalter is really no different than if it were to insist on the use of a certain prayer book. It is an unnecessary binding.
I don't think this is necessarily the case. At any rate, I don't think it can be sustained that the Presbyterians and Puritans of the 17th century objected to the prayer book on the grounds that it was too much uniformity, but rather on the grounds that it violated the RPW. They were all for uniformity of worship across churches, as can be seen by their various national covenants calling for covenanted uniformity, as well as by the Directory for Public Worship which they produced, and the Psalter which they commissioned.
From The Solemn League and Covenant:
That we shall sincerely, really, and constantly, through the grace of GOD, endeavor, in our several places and callings, the preservation of the reformed religion in the Church of Scotland, in doctrine, worship, discipline, and government, against our common enemies; the reformation of religion in the kingdoms of England and Ireland, in doctrine, worship, discipline, and government, according to the Word of GOD, and the example of the best reformed Churches; and shall endeavour to bring the Churches of GOD in the three kingdoms to the nearest conjunction and uniformity in religion, Confession of Faith, Form of Church Government, Directory for Worship and Catechising; that we, and our posterity after us, may, as brethren, live in faith and love, and the Lord may delight to dwell in the midst of us.