I do believe there is reason to believe that the Nazis exaggerated the number of Jews deported though. The Nazis wanted to make it look good to higher ups that they were doing a good job deporting a bunch of Jews, which is why it may have been exaggerated. This article also gives some other arguments:
https://en.metapedia.org/wiki/Korherr_Report
Now one may argue that I'm just making stuff up to fit a theory I have. Even if that were true, they still have to "explain away" the deportations as really being about killing. So they are no better in that regard. Although I don't think I'm just making stuff up out of thin air. We do have reason to believe that Einsatzgruppen reports exaggerated the amount of Jews killed.
In The Origins of the Final Solution, Browning cites an example where a German official did over-estimate the number of Jews shot on the Eastern Front by German forces. The over-estimation is contained in the "Hahn summary report" of December 10, 1941. Five Einsatzgruppen reports were summarized by Franz Rademacher's assistant, Fritz Gebhard von Hahn. At this point we let Browning continue with his story: "He [Hahn] extrapolated, however, from the examples of EK 2 and 3 in the Baltic, and wrongly, concluded that each individual Sonderkommado had on average liquidated 70,000 -80,000 Jews. The result was an over- rather than underestimate of the number of Jews murdered, but clearly Hahn had not failed to grasp the significance of the reports concerning the intended fate of Soviet Jewry [p. 402]."
https://codoh.com/library/document/the- ... topher/en/
So if we know this happened in other cases, it is not unreasonable to assume it happens elsewhere.