This assertion is of course not a dogma in the sense of theology, but a statement that can broadly be described as such, in other respects.
As a JW one reads and studies basically with the WTS's own Holy Scripture. In general, nothing would stand in the way of this if one did not know that the New World translation, as it is officially called, is sometimes even bent over in its explanations. A Jehovah's Witness of Field, forest and meadows serfdom, i.e. an "Otto Normal Consumer" of this denomination, has no idea that this is the case. Even elders are usually just as ignorant of this fact.
The WTS, of course, argues the other way around. From there the premises apply,
a) our translation is literal and accurate (which is often true, but not always),
b) it is written in modern and therefore understandable language (apart from some "screwed" formulations, which are a bit bumpy) and
c) which is the most important of all (from WTS point of view), the name "Jehovah's" is honored by reinsertion unlike most other translations.
Let's take a closer look at these statements.
"The New World translation is literal and accurate." Generally it can be said, yes, that is correct as long as the actual statements of the HS agree with those of the official teachings of the WTS. If there are discrepancies, bending takes place. Bent to create formulations that seem to be one with the teachings of WTS. A serious example of this has already been shown under Dogma 6. A "and in the houses" was transformed into a "house to house" because it comes much closer to the WTS doctrine that their little sheep have to do a door-to-door service. This provides "evidence" that one's own teaching is correct. Or that already mentioned above in Dogma 3 "coup de main" with the diffraction of "broke the bread" to "took their meals" ditto. One could also mention several such examples in which simply "reconfigured" was done. As already mentioned above, Ray Franz brings in his books several such examples, which prove this here. This is one reason why the JW are forbidden to read such books. If only they would get behind the tricks of their society.
"It is written in modern and therefore understandable language". That is a lot of translations today. Of course, if you compare the NWT with an old Alioli Bible from the last century or with an old Luther translation from primeval times, it is clear who is the "winner" here and now. If, however, modern translations - and I'm not talking about the much controversial "Volx Bible" here - are placed next to them, then things look quite different.
"The name Jehovah has been inserted." Then it is rather the case that in the overall picture some other translations, such as the butchers, are much better, although or because [RH] it does not have the name Jehovah in its repertoire, like the NWT, which in overzealousness propagates the name of God, who is actually more Yahweh than Jehovah, even in places where it is not in the original. Especially in the New Testament, where only Kyrion can be read, so Lord and not Yahweh, or even Jesus is meant by this expression. Although the NWT in its appendix contains some arguments that are supposed to underpin its teaching, this does not change the fact that its arguments result in quite a patchwork that has been artificially cobbled together.
Since, by the way, the WTS regards the cross as a pagan symbol, in the same Bible, as well as in the appendix, the image of a crux simplex is shown, a stake of torture at which a condemned person is executed, with a "proof" that its doctrine is correct and therefore no "real" cross, a crux duplex, was used for the execution of Jesus. Unfortunately it is omitted that in the same book, from which this representation was taken, already a few pages further also such was illustrated, with an execution of a "perpetrator". One should just know that both versions of executions are "on file" and were at disposal and not only one. In addition: What difference does it make how Christ died (in which posture): hands left and right of the body or above his head? What is important is that he shed his blood for us human beings.