I'm not sure what your point is. In your opening post you asked specifically about the infin. passive of 3rd conj. verbs, not infin. passives generally.But then what of the passive infinitives of the regular thematic verbs? Any complete explanation would have to explain both.
Leaving aside the earlier by-forms with -ier -rier endings, passive infinitives are originally dative sing. of either a root stem (cogi etc.) or an S-stem, e.g. ama-ri (Old Latin ama-rei) from *ama-sai, vide-ri from *wide-sai.