When someone says, "both can be true," they really need to say what the two things are, exactly.
Me, too. But there is no contradiction in assuming multiple uniformed services being combined into one, including one or more that are not armed. The US has 8 uniformed services, 6 armed (Army, Navy, Air Force, Marine Corps, Space Force, Coast Guard) and 2 not armed (National Oceanic and Atmospheric Administration and Public Health Service) [https://www.govinfo.gov/content/pkg/USCODE-2020-title37/html/USCODE-2020-title37-chap1-sec101.htm].I always took it to mean all military branches were combined to become Starfleet.