The Rambam wrote ונאמר לא בשמים היא הא למדת שאין נביא רשאי לחדש דבר - From לא בשמים היא we learn that a Navi may not innovate any new laws. We asked earlier that this is difficult because the correct source for אין נביא רשאי לחדש is אלה המצוות and not לא בשמים היא?
It would seem that according to the Rambam the pasuk of אלה המצוות is not an exclusion regarding נבואה which would make the pasuk אלה המצוות a halacha about נבואה but rather it fits with the opinion of the Rambam [Mamrim Chapter 2] that there is an איסור of בל תוסיף when the rabbis make fences [סייגים] and the only time they have the authority to make fences is when they tell us that they are making a rabbinic fence. The pasuk אלה המצות is telling us that there cannot even be an איסור דרבנן or an איסור from a Navi and when they do decree איסורים as a fence they must make it clear that it is from them and not from the Torah. But otherwise, it is forbidden for them to add mitzvos, even if they are not adding on to the Torah. [See the Ritzva Rosh Hashana 16b and the Maharal Be'er Hagolah Maamar Aleph]
A source for this would be the Yerushalmi [Megilla 1/5] אלה המצות - אלו המצוות נצטוינו מפי משה וכך אמר לנו משה אין נביא אחר רשאי לחדש דבר מעתה [see there in the gemara what it says about Mikra Megilla]. So we see that it is a general exclusion about mitzvos - these mitzvos we were commanded from Moshe [and no others] and from there we learn that a Navi may not add on mitzvos but it is not an exclusion regarding nevuah per se.
According to this we can say that when the Rambam [in halacha aleph] quoted the pasuk of לא בשמים היא even though the halacha that a Navi is not allowed to be מחדש is learned from אלה המצוות he intended to explain why the כח הנבואה shouldn't have the same status as rabbinic fences which are not considered forbidden addtions to the Torah. Because as we said, אלה המצוות is a halacha in the realm of בל תוסיף so as long as there is no בל תוסיף problem a Navi should be allowed to teach us a new din. Therefore the Rambam writes לא בשמים היא meaning that the fences of the rabbis are similar to the כח of the חכמים in the world of logic and analysis where it is given over to their intellect and not בשמים. Automatically, anyone who claims to have received נבואה about a new law is a Navi Sheker and executed because such laws cannot come from a Navi and שמים.
Once we learn from the pasuk אלה המצוות that a Navi may not add new laws, anything he adds is subsumed under the more broad category of לא בשמים היא. The pasuk אלה המצוות teaches us that the innovation of a Navi is בל תוסיף and ממילא is encompassed by לא בשמים היא - they don't have that power. Since the Rambam is discussing איסורי נבואה he omitted the pasuk of אלה המצות [which is telling us a din in the realm of בל תוסיף] and instead quoted the pasuk לא בשמים היא which relates directly to איסורי נבואה.