There is, indeed, a modification to the Sola Scriptura stance of the Reformers. You quote one such modern take on it which means that either it is true, or the original stance is true, but they both cannot be true! You have spotted a crucial difference and it deserves attention. In your comment where you cite Lesley's answer, you spot from that Lutheran quotation a subtle deviation from the original Sola Scriptura.
Alas, it will be so hard for me to pin down WHEN this modification happened, rather than WHY; I shall give the former a near-total body-swerve. But in my quotes, it should become clear that a cerebral approach to Scripture that allows our imaginations to take over is the underlying reason why. Whenever people treat Scripture purely as a book that tells everybody everything to do with salvation and religious forms, then it either becomes a closed book, or a means of producing interpretations that become a form of legalism than the Bible itself warns Christians against.
This first quote is from John Calvin (1509-64), the leading 16th century theologian of the European Reformation, who laid a foundation for biblical studies and systematic theology still widely used to this day. Alas, I have no source for this quote so if anyone can provide it, I shall be grateful:
"No sooner do we gain some slight knowledge of God from looking at the world, than we turn from the true God and set up in his place an imaginary vision from our own brain. We draw the worship of justice, wisdom and goodness away from the fountainhead, transferring it elsewhere."
Now, here is what Martin Luther (1483-1546) said about channels of self-disclosure which God has ordained for man – the Word and the Sacraments. Yet the Word is not to be equated with Scripture nor with the Sacraments, though it operates through them and not apart from them. The ‘Word’ is not the Bible as a written book because:
“The gospel is really not that which is contained in books and composed in letters, but rather an oral preaching and a living word, a voice which resounds throughout the whole world and is publicly proclaimed.”
This Word must be heard. This Word must be pondered:
“Not through thought, wisdom, and will does the faith of Christ arise
in us, but through an incomprehensible and hidden operation of the
Spirit, which is given by faith in Christ only at the hearing of the
Word and without any other work of ours.”
More, too, than mere reading is required:
“No one is taught through much reading and thinking. There is a much
higher school where one learns God’s Word. One must go into the
wilderness. Then Christ comes and one becomes able to judge the
world.”
Likewise, faith is given to those who avail themselves of those outward rites which, again, God has ordained as organs of revelation, the Sacraments. Speaking of God and how he can be ‘found’ in the material creation, Luther made clear that:
“…yet he does not wish me to seek him apart from the Word… He is
everywhere, but he does not desire that you should seek everywhere but
only where the Word is. There if you seek him you will truly find,
namely in the Word. These people do not know and see who say that it
doesn’t make sense that Christ should be in bread and wine. Of course
Christ is with me in prison and the martyr’s death, else where should
I be. He is truly present there with the Word, yet not in the same
sense as in the sacrament, because he has attached his body and blood
to the Word and in bread and wine is bodily to be received.”
Luther maintained that true Christianity is apprehended by faith channelled through Scripture, preaching, and Sacrament. That is why he avidly promoted the study of Scripture in church and school. In church, the pulpit and the altar must each sustain the other. That is why Luther would create dismay by going on at length about a single point of doctrine. People thought he could be unreasonable to risk severing friendship over one such point, but he equated that with saying it was unreasonable to sever friendship over a single point of strangling one’s wife or child. To deny God in one point is to attack God in all. Right doctrine is only obtained through Scripture alone as disclosed via the Word of God. And Christ is the sole revealer. A Christless approach to Scripture will result in corruptions. Source: ‘Here I Stand’ Roland Bainton, pp224-5 (Lion 1988 reprint, Britain)
Now, back to John Calvin for some quotes of his regarding the sole authority of Scripture:
“They place the authority of the church without the word of God: we
annex it to the word, and allow it not to be separated from it.”
(Institutes 4.8.13)
By ‘They’ he meant churchmen who claimed that church tradition was an equal source of authority to the Bible. By saying they annex tradition to the word, this meant subjecting tradition to the word and not allowing tradition to stand alone from it.
“…God claims it as his own peculiar privilege to rule us by his laws
…it is unlawful to transfer to man what God declares to belong only to
himself …this completely cuts off all the power claimed by those who
would take it upon them to order anything in the church without
authority from the word of God.” (Institutes 4.10.7)
“It is the will of the Lord that we shall depend wholly on his word,
and that our knowledge shall be confined within its limits; and
therefore, if we lend our ears to others, we take a liberty which he
has forbidden, and offer to him a gross insult.” (Commentary on Isaiah
8:20)
I suspect that the earliest and faintest deviations from such a Reformed stance on Sola Scriptura might have begun with the Lutheran branch of Protestantism, long ago, but certainly by the time James Arminius died in 1610 it became clear that some had different interpretations of what the Scriptures meant.
The Arminians made a Remonstrance - or protest - to the Dutch Parliament, to change the Reformed position as set out in the Belgic and Heidelberg Confessions of Faith, with respect to five points. And this might be another clue as to deviations - the importance attached to Confessions of Faith, which seem to expand on what Scripture teaches, the better to clarify, yet they so often lead to divisions.
The National Synod of Dort sat for 154 sessions over a period of seven months, seeking to reconcile the Arminian viewpoint with that stated in the Scriptures, but could not do so. Let me give the last word on Sola Scriptura to Charles Haddon Spurgeon whose declaration brings us back to Luther's view of Christ as the sole revealer of Scripture:
"It is no novelty, then, that I am preaching; no new doctrine. I love
to proclaim those strong old doctrines that are nicknamed Calvinism,
but which are surely and verily the revealed truth of God as it is in
Christ Jesus."