From back in the day, it was always considered "not cool" to hotlink- i.e. have your HTML reference images that someone else is hosting.
I'm trying to be clear on the etiquette around oEmbed, however. Since it seems like the point of offering oEmbed is to let you do just that - embed their content on your site- does that mean that "hotlinking" an image from a site's oEmbed is "okay?" Or at least, that it's OK so long as you're using it for the intended purpose, i.e. clearly representing it as embedded content from their site?
Also - if the answer to the above is "yes it's okay," are there cases where one should consider not doing it anyway (and instead downloading a copy to your own server), and if so why?