The mishna said that after the burial, if there is enough time to read shema before the shura is formed, the attendees must read, but if not they are exempt. The reason that they are exempt is because they are still considered to be involved with a mitzvah. Although the mitzvah of burial is over, the shura is a part of the mitzvah of nichum aveilim. Rabbeinu Yona explains that נחום אבלים is also considered a d'roaysa mitzvah because it is included in gemilas chasadim and supported by the pasuk of והודעת להם את הדרך, therefore we can apply the principal of עוסק במצוה פטור מן המצוה to even exempt from a mitzvah d'oraysa such as krias shema.
Rabbeinu Yona clearly assumes that involvement in a mitzvah d'rabonon wouldn't exempt from a mitzvah d'oraysa, but we consider nichum aveilim to be d'oraysa. Rav Elchonon Wasserman (Koveitz Shiurim 2:32) raises a question as to whether one involved in a mitzvah d'rabonon would be exempt from a Torah mitzvah, but doesn't cite Rabbeinu Yona.
However, the Mishna says that if there would be enough time before the shura is formed to say shema, they must do that. The gemara explains that even if there isn't enough time to say the entire shema, just one perek or even just one pasuk, they must do that. Now, if we assume that when the gemara says 13b that Rebbi would say שמע ישראל ה' אלקינו ה' אחד in middle of his shiur, it means only that one pasuk because only one pasuk is d'oraysa, it would make sense that we require the menachamim to say even one pasuk. However, according to Rabbeinu Yona who holds that the entire perek is necessary m'doraysa, and certainly according to those who hold that both parshiyos are d'oraysa, why would we make the menachamim say just the pasuk of shema?
It seems that the mitzvah of shema may not be fulfilled unless both parshiyos are said, but it is not all or nothing. Although there is no independent mitzvah to be מקבל עול מלכות שמים, rather it is part of the mitzvah of shema, if one fulfills that aspect, they have fulfilled a mitzvah d'oraysa - just that they are missing the other component of the mitzvah. To properly fulfill the mitzvah of shema one would need say both parshiyos to even be mekabel עול מצות, if not they should at least say the entire section of shema to be מקבל עול מלכות שמים properly, but if not there is still a kiyum of kabalas עול מלכות שמים that is achieved by saying the first pasuk.