The present account focuses on a transitory circumstantial state (ḥāl muntaqila): a condition accompanying a particular event, not necessarily a permanent characteristic. In جَاءَ زَيْدٌ رَاكِبًا, being mounted describes the manner of Zayd's arrival.
A confirmatory ḥāl, in contrast, may reinforce a meaning already established by the construction. Since their discourse functions differ, one should not mechanically extend every rule illustrated by a transitory circumstance to an emphatic one.