Summary: It seems that you and the grammarian interpret the word "active" differently, and that seems to be the source of all confusion. The defining feature of deponent verbs is the semantics of the subject, and I could well call this "active meaning". It has nothing to do with how active some action is in practice.
It seems that we have three relevant dichotomies here: deponent–non-deponent, transitive–intransitive, and active–passive. By the last one I mean "active" verbs that describe an action (like jumping or speaking) and "passive" verbs that describe a state or change thereof (like being red or being born). This has nothing to do with active and passive forms of a verb. I assume this is what you mean by active and passive (meaning) in your question; please clarify if I misunderstood.
The three dichotomies are mostly unrelated. The only restriction seems to be that a passive verb cannot be transitive; I cannot quite fathom what a transitive passive verb could mean. The other combinations are possible:
- deponent transitive active: sequi
- deponent intransitive active: loquor
- deponent intransitive passive: nascor
- non-deponent transitive active: trahere
- non-deponent intransitive active: fluere
- non-deponent intransitive passive: rubere
Notice that I speak of active and passive meaning, not active and passive forms. In this answer I will only treat active forms of non-deponent verbs and passive forms of deponent verbs (only forms in the "principal voice" of any given verb, if you will). I would not confuse passive forms into this discussion. Passivization of verbs with two objects might be of interest.
I see no connection between deponency and activity in either direction. There might be correlations, as the six classes above are not equal in size, but I wouldn't draw conclusions from it.
Lucanus in Bellum civile uses locuto Caesare. I think loqui is rarer in this use than mori, but I can't see why it'd be impossible. Similarly agmine secuto of Annius Florus looks like an absolute ablative of a transitive deponent verb. Absolute ablatives of certain kinds of deponent verbs might well be rare, but I cannot see why they would be impossible.
I think the point is that you have misunderstood "active meaning". Passive forms of non-deponent verbs work so that the semantic object is the syntactical subject, whereas in active forms semantics and syntax agree. For deponent verbs all forms are passive (apart form the present participle), but still the syntactical subject is the semantic subject. This relation between semantic and syntactical subjects is what "active meaning" refers to, not "activity" in the sense of making a conscious decision to act or anything like that. The bold-faced part above is what I would give as a more proper definition of a deponent verb, but I might certainly summarize it less rigorously as "deponent verbs have passive forms but active meaning".
In the definition of a deponent verb you cite, "active meaning" means that semantics and syntax agree on the subject like they do for active forms of non-deponent verbs. This can indeed be misleading or confusing. The point here is that "active" is related to active and passive forms, not "being active".