Local images
<img src="/images/someimage.jpg">
Not local images
<img src="http://www.someotherdomain.com/images/someimage.jpg">
If you are using the second option then he is correct. It will cause a huge slowdown if the other sites are slow. You should always host images displayed on your site yourself. There are instances where that isn't possible and you'll have to live with the slow downs or put them in an iframe. That way the page loads and the slow images can load on their own time.
If you are indeed hosting all of your images then you most likely have some server configuration issues going on. I highly suspect, based on his statement, that you are linking images from other sites and that is causing the slow downs. Hope this helps.