"Every Baptist church being, in organization, a church complete in itself, and, in no way organically connected with any other church, such a thing as one church succeeding another, as the second link of a chain is added to and succeeds the first, or, as one Romish or Episcopal church succeeds another, is utterly foreign to and incompatible with Baptist church polity. Therefore, the talk about every link "jingling in the succession chain from the banks of the Jordan to the present," is ignorance or dust-throwing."~ W. A. Jarrell
The history behind this statement is interesting. Jarrell, Christian, Graves, Dayton and others were in an ongoing written debate with those who believed that Baptist originated in England with the reintroduction of immersion after 1641 (Whitsitt, etc.).
The debate had come down to demanding that if Baptists did not originate in 1641 in England but came down from the time of the Apostles, and that Baptist churches were constituted according to the definition of J.R. Graves which was defended by J.M Pendleton and published in The Baptist Enclyopedia by William Cathcart in the following summary:
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The doctrine of landmarkism is that baptism and church membership precede the preaching of the gospel, even as they precede communion at the Lord’s table. The argument is that Scriptural authority to preach emanates, under God, from a gospel church; that as “a visible church is a congregation of baptized believers,” etc., it follows that no Pedobaptist organization is a church in the Scriptural sense of the term, and that therefore Scriptural authority to preach cannot proceed from such an organization." William Cathcart, The Baptist Encyclopedia "Old-Landmarkism"
then their opponents demanded historical link by link evidence. In response to this demand, Landmarkers denied than any link by link historical evidence was necessary or needed for present day churches to be recognized as apostolic in origin or that there was sufficient historical evidence to prove they did.
Jarrell went on his book to defend a link by link succession of Baptist GROUPS instead of a link by link successoin of Baptist Churches.
The position of Jarrell and other Landmarkers was if it walks like a duck, talks like a duck and looks like a duck it is because it is a duck and has come from ducks. Graves and others used the analogy of the cable that had recently been laid across the Alantic Ocean from Europe to America to defend the same point. Some used the analogy of an underground river, etc.
All equally denied that link by link evidence was necessary to prove a church was apostolic in origin. However, none denied that if there was sufficient history that such a case could be proved. Dr. J.T. Christian makes this affirmation in the preface of his first volume on Baptist History. Jarrel makes this argument by defending each group century by century back to the apostlic century as essentially Baptist in doctrine.
Hence, if you know the background of this written debate and what their opponents were demanding to support their ecclesiastical position based upon scripture then you can better understand their responses in their written defense.
BTW J.R. Graves made the same denial as Jarrell in his book "Old Landmarkism, What is it?