I used to have the same problem with images here on E; images that I hotlinked to their spots on an external site (a photo upload site etc), or any off-E location, wouldn't show up here, not even when scrupulously following template scripts or simply using QUOTE from some other post where someone had embedded a picture link, retrieving what they had written, copying it and just inserting my own pic link instead. I know how to use the img tags and so on, and never had this issue on other sites. Eventually the issue vanished and I was able to hotlink pics for profiles etc like most everybody else, but despite asking helpful people here and trying out a couple of ideas there was never any real answer to why it had happened.
What I do think happens sometimes is that an image stored on a web server may have different URLs to different viewers in different countries or continents. For the image to appear here on E's pages, it will have to be located by Elliquiy's servers which are in America. Normally the URL address is supposed to take anyone (a page, a server or a person) to the file, but sometimes, due to how the net is constructed, a file or a page will appear with different URLs seen from different places. So you'd copy-paste the address where the image shows up seen from let's say France, Brazil or even Florida, but the servers are in let's say California and won't find anything at that location. I'm fairly sure that's what happened to me a few times with picture files for a character sheet where another member said: I can see it if I'm linking it to this precise address, this is what I wrote to get your sheet to show up with the pic, this is what should be hotlinked and it works for me - and that address didn't work when I used it on its own, though the preview of the character sheet did show up. The inverse was also true: if I sent her what I had typed so that she could see the code template (which was mostly the same of course) she didn't get to see the picture. And it turned out that we seemed to be using two different URLs for the same uploaded picture file, each of us using the url path that the pic would have to her (though they were on the same site of course).
I don't know how common it is to get that kind of "relativity of URLs" but my hunch is it could be a growing problem as the internet expands and becomes more complex and multi-platform.