I am afraid that whilst this may be a popular view within some evangelical and Reformed groups it is in fact incorrect. I would refer you to James VanderKam's article "Questions of Canon Viewed through the Dead Sea Scrolls" which is available to read online. Do check out
The Canon Debate edited by Lee McDonald and James Sanders and also
The Dead Sea Scrolls and the Origins of the Bible by Eugene Ulrich. But this is in someway to confuse the issue, what we find within second Temple Judaism is that whilst certain books were held to be authoritative this did not mean that the texts of these books were set. There are two simple examples; the first is found in the Pentateuch and the second in the prophets.
Exodus
There are three primary textual families; (1) Masoretic Text or MT, (2) Septuagint or LXX, and (3) Samaritan Pentateuch or SP. Of these the text of the MT, LXX and SP do not equate with one another. At Qumran manuscripts were discovered that supported each of these three textual streams, the most important being 4QpaleoExod^m which is substantively the SP minus the theological changes made by the Samaritans and which demonstrates that in early Judaism two books of Exodus were in circulation; one which was similar to the MT & LXX and the other similar to the SP.
This means that it is incorrect to state that there existed an original text of Exodus, rather there is a pluriformity of texts, or multiple literary editions. As such the theory of an original autograph is very difficult, if not impossible, to square with the textual evidence.
Jeremiah
The LXX version of Jeremiah and the MT version are quite different, the former is far shorter than the latter and some chapters are in a different order. At Qumran there are four manuscripts that are important; 4QJer^b and 4QJer^d which support the LXX and 4QJer^a and 4QJer^c which support the MT. This implies that in early Judaism two, substantially different, books of Jeremiah were in circulation. Again this undermines the theory of an original autograph.
What is also important here is to keep in mind that the writers of the New Testament quoted the LXX and the Alexandrian Jews used this as their Scripture.
The "canon" of the Hebrew Bible was still an open issue during the NT period and there is evidence that the Jews did not settle this question until around 200 C.E. What is certain however is summed up here by VanderKam:
As nearly as we can tell, there was no canon of scripture in Second Temple Judaism. That is, before 70 CE, no authoritative body of which we know drew up a list of books that alone were regarded as supremely authoritative, a list from which none could be subtracted and to which none could be added.