On the one hand, I agree that fundamentalism was, in a sense, itself modernist and quite influenced by modern assumptions about the meaning of texts and the necessity of strict literalism, putting modern assumptions on ancient writers. Thus when it is pointed out that there are gaps in biblical genealogies and Matthew was not saying that there were literally only 14 generations from Abraham to David, or that it's not necessary for Creation to have happened in 4004 B.C. and we don't need to know the exact date, people might look at you askance or act troubled as if such an idea threatens the reliability/inerrancy of Scripture.
But that doesn't threaten inerrancy, it just means you shouldn't put modernist assumptions into the definition of inerrancy. The Biblical authors didn't report everything with scientific precision, or in the exact order they occurred necessarily.
On the other hand, I think this type of argument is overblown when used against inerrancy itself; "inerrant in the original manuscripts" is simply a more precise definition of what most Christians have usually believed; for one thing, modernist ideas specifically challenge the reliability of Scripture and often careful definition is needed. Precision in definitions is probably a feature of the modern world; but that's because modern minds seem to demand it. Without precision, moderns seem to get confused and start conflating different things - for example, immediately point to errors in translation or manuscript transmission as evidence that the Bible is not inerrant, and therefore it doesn't matter if they decide the Bible is wrong about homosexuality, the character of God, the historicity of the OT - like maybe David and Moses never existed and it was all made up post-exile, etc.
Take this discussion of Scripture from someone who lived over 1200 years before rationalism began, for instance. Whatever else Augustine was, at least no one can accuse him of being a modernist:
For I confess to your Charity that I have learned to yield this respect and honour only to the canonical books of Scripture: of these alone do I most firmly believe that the authors were completely free from error. And if in these writings I am perplexed by anything which appears to me opposed to truth, I do not hesitate to suppose that either the manuscript is faulty, or the translator has not caught the meaning of what was said, or I myself have failed to understand it. As to all other writings, in reading them, however great the superiority of the authors to myself in sanctity and learning, I do not accept their teaching as true on the mere ground of the opinion being held by them; but only because they have succeeded in convincing my judgment of its truth either by means of these canonical writings themselves, or by arguments addressed to my reason. I believe, my brother, that this is your own opinion as well as mine. I do not need to say that I do not suppose you to wish your books to be read like those of prophets or of apostles, concerning which it would be wrong to doubt that they are free from error.
The authors being without error, but not the subsequent copied manuscripts or the translations, is pretty much exactly the definition of inerrancy in the original manuscripts. It sets the parameters, defines the playing field, for discussion of the meaning and application of Scripture. If you wonder if something your copy of Scripture is accurate, you can check other translations, do some digging to see if the copyists could have made an error, look around at other interpretations to see if you misunderstood, or just accept that what it seems to be saying is accurate.