I personally don't want to characterize my Baptist brethren's view of baptism as "incredibly low." In certain respects, it is lower compared to mine in my perspective. I'm not sure the Baptist and I could fully agree on some objective perspective for the both of us to share.
And, I suspect it is the case that there is a presentation of the Baptist Confession stance that adds something to the bare "testimony to the congregation" takeaway.
It is part of the difference in the Presbyterian and the common Baptist perspective, to note that "Who is the primary speaker in baptism?" makes for a fairly fundamental divide in understanding.
-----If baptism is first and foremost a personal, individual public witness --a man's statement-- then the church participates, facilitates, and validates that claim.
-----If baptism is first and foremost the church's welcome and declaration of incorporation, then the personal (or in the case of parents, for the baptized) affirmation is the reply or answer.
These two priorities seem to me set in view two distinct starting points, two understandings of the nature of baptism; but also expose some differences in what the church is about, the meaning of its ministry.
This is not saying--and I'm glad it isn't--there is no overlap in the content of what Baptists affirm about baptism and the church, and what Presbyterians affirm. But it makes a difference where one starts; it makes a difference how one puts the material together in a collection. The picture that's assembled at the end looks a little different to each examination, and definitely the other collection does not seem as coherent to the opposite collector.
In the Presbyterian's theology, the church (the minister) is serving, as he regularly does in all his other formal activity in worship, as God's spokesman. He is speaking for God, or on the part of God. That is an important element of what we understand the church's job is in the world--representing God in Christ to the world. There are lots of ways the church speaks in God's name, including many informal ways by which individual Christians do this. But then there are the formal and public ways, and that is a responsibility that should be accompanied by ordination to that role or task.
So, in baptism the Presbyterian church's intent, meaning the minister's intent, is to declare this baptized person a member of the church, a disciple of Christ; and to proclaim the promise of God, (here I'm borrowing the Heidelberg Catechism Ans.#69) "that I am as certainly washed by his blood and Spirit from all the pollution of my soul, that is, from all my sins, as I am washed externally with water, by which the filthiness of the body is commonly washed away."
Understand: God will do this for the believer. When any baptized person so testifies to his sure conviction of this, saying "I, myself, I am certainly..."--regardless of when he was baptized and the promise was declared--he claims to believe in God's word of promise which baptism declares.
The promise of God is for believers. It is declared to be The Case, regardless of whether it is accepted or not. The certainty of the promise is not dependent on the faith of anyone. Unless someone knows by prophecy what exactly will happen, by whom, to whom, etc., there is nothing in the Bible that assures anyone of his personal title to any promise of God irrespective of his belief and hope.
So, we should not be misunderstood to say that God, in baptism, has just promised Adult John Doe or Infant John Doe-- "You ARE a child of God, you ARE going to heaven." That is NOT the promise of God, it is not from the Bible. It is not the claim... unless he happens to be a crypto-RomanCatholic, or possibly an Anglican, or a Lutheran, someone who holds to some form of baptismal regeneration. But that doctrine is contrary to our Confession.
This is what makes baptism a seal: its promissory character. Now, the Spirit of God alone applies that seal in the secret place, and does it for his elect. What men see with their eyes is a sign, pointing to the things that baptism signifies. It is a "seal" also, but only in the sense that there (as it were upon the paper) the authenticating mark of the King's signet has been placed to visibly mark his property and his claim. Because of the kind of seal it is, affixed by the hand of a man, it could be invalidated. But insofar as the secret seal is set by the design of the Holy Spirit, that is an irrevocable seal. "The Lord knoweth them that are his," 2Tim.2:19.
When His seal is apprehended by faith, then it is effectual. When the sign is appreciated by faith, then the promise is accessible to him that can comprehend and read the sign. The things that are signified by baptism belong especially to him that is baptized. Of course, those things could also belong to some elect person who has not (for any reason) not had the privilege of baptism, precisely because it is faith in those things signified that mean possession of them. But the value of the sign is how God has united it with the things signified.
Imagine the uselessness, or even the condemnation, of possessing the sign of something of God's, and making no use of it, misusing it, devaluing it, or even execrating it. It is why possession only of the sign of a thing (when accounting is made), is so damnable, regardless of how one came to possess it, see 2Sam.1:5, 10, 15.