Your suspicions are all on target. On page 114 of Studies in Maimonides and His Interpreters, Prof. Marc Shapiro notes that Rambam omits the statement in Berakhot 18a since in his view:
Dead people do not observe the actions of people.[i] Furthermore, as Maimonides could well point out, the Talmud never indicates that this is a generally applicable law rather than simply a conversation between two amoraim.
He further notes there that while Rambam does quote the teaching regarding tefillin, Torah scrolls and Sh'ma in a graveyard, (which unlike the statement about tsitsit, is phrased as an explicit instruction), he does not actually mention loeg larash.
Indeed, R. Qafih notes (Ketavim Vol. II pg. 622, and commentary to Hilkhot Evel, pg. 217) that following his general approach, Rambam did not present the Bavli's reason for not saying Sh'ma in a graveyard and the like, but instead explained it based on the dirtiness and impurity of graveyards, as is clear from Hilkhot Tefilla (4:8). R. Qafih further notes (Ketavim pg. 625 and commentary to Hilkhot Evel, pg. 219) that this understanding that the problem with Sh'ma in a cemetery is the impurity, is implied by the Yerushalmi Moed Kattan (3:5). R. Qafih proceeds to discuss the general point (which some may find surprising) that Rambam's worldview would lead him to reject an idea in Hazal, and how it is consistent with that of Rambam's predecessors. This is also a major subject of Prof. Shapiro's entire book, and is discusses in R. Dr. Isadore Twersky's Introduction to the Code of Maimonides, as well.
See also this piece by R. Moshe Tsuriel which references R. Qafih, and discusses the propriety of different activities in cemeteries.
It should be noted that there were other commentators who felt the need to reconcile Rambam with the Bavli. Much of the writings of R. Qafih, and Marc Shapiro's book, address this general approach of not learning Rambam qua Rambam.
[i] While Prof. Shapiro (and R. Qafih who will be cited) doesn't demonstrate this there, (perhaps he does elsewhere), it is important to note that after R. Hiyya chided R. Yonatan for dragging his tsitsit in the graveyard, R. Yonatan defended himself (and this defense provides another reason why Rambam might not record an injunction on tsitsit in a cemetery; R. Yonatan evidently didn't hold of one, and even after R. Hiyya mentioned it, he provided reasoning against it, although the Gemara later claims (18b) he retracted, the extent of this retraction is debatable, and the Yerushalmi Berakhot (2:3) does not record him retracting). R. Yonatan claimed that the dead are not aware of the goings on in the world to justify not bringing in tsitsit! He bases himself on the verse "The dead know naught" (Ecclesiastes 9:5). R. Hiyya rebuts this with a seemingly more Midrashic interpretation. However, the simple understanding of the verse, in line with R. Yonatan's position of bringing tsitsit into a cemetery, is still cited by Rishonim in Rambam's milieu, such as R. Yehuda ibn Bil'am to Isaiah (8:19), Radak there, and Ibn Ezra to Ecclesiastes there.