Yes, you are well informed. We do use "pasar por" to mean "stop by" as in "Paso por Walgreens y voy a tu casa." - "I'll stop by at Walgreens and then I go to your house."
But in this case it doesn't work like that, normally it has that meaning when it's "paso por" if it's me, and "pasa por" if you're telling someone to stop somewhere or you're telling them that someone will stop somewhere and then go somewhere. I'm not very good explaining but if you need more clarification just ask. :)
It actually work in all tenses
Paso por la tienda y te busco. - I'll stop by the store and then I pick you up.
Pasa por la tienda y buscalo. - Stop by the store and pick it up.
Pasé por la tienda y después lo busqué. - I stopped by the store and then I picked him up.
Pasaré/voy a pasar por la tienda y después lo busco. - I will/am going to stop by the store and then I'll pick him up.
So I'd say it doesn't work with progressive verbs.
Well I put "walking" by the hotel [by accident, what trips me up is i'll make a translation that has the same gist but not the same exact meaning] and it accepted it. Since pasando = passing, i'll assume they're just accepting other verbs that one might use that have the same gist meaning, if not literal meaning... however, this is a case where they actually shouldn't be doing that
In one of the "choose the correct ones from these three", I checked driving and, after thinking a bit, omitted walking. It was counted wrong. So, walking is not accepted only in this one exercise. The next person that can, please click the problem button and check "my translation should be accepted".
Not a NS but I'll give it a shot: Está pasando/sucediendo cerca del hotel And I think I see what you're getting at. . . Pasar in this case translates as 'to happen', but the 'by' (which also means 'close' or 'near' in this sentence) gets translated into 'cerca de'. . . For the sentence in the lesson, the propositions that we use in English with 'pass' (by, through) are included in the verb pasar and further clarified through context. . . Am I getting this??