Again semantics. You are attempting to split hairs based on distribution opposed to type. This is like being a pedant over someone referring to tissues as a Kleenex despite it not being that particular brand. Podcasts were ambiguous back when they were still new, too.

Shoutcast servers were/hosted digital broadcasts. Podcasts were containerized (aka offline) recordings of these. You could argue that calling a live show a podcast is technically incorrect: but thanks to language continuing to adapt to its environment… You’d actually just be out of date or misinformed.