Not true. I do it all the time. Though I have yet to use TinyPic.com to host my product pics, I use a couple of other free hosting sites as well as my own Comcast server space that my ISP gives me. All you need to do is put the HTML tag in the section where your description goes when building the listing on eBay.
So, at the end of your description, to get 3 photos in your ad, you would place a string that looks like this:
<img src="http://www.tinypic.com/your-photo1.jpg">
<img src="http://www.tinypic.com/your-photo2.jpg">
<img src="http://www.tinypic.com/your-photo3.jpg">
That's it. Ebay doesn't block that type of HTML code in a listing. And with TinyPic.com, you don't have to worry about clearing off the pics from the server when the auction ends. Just upload it and forget it.
Thanks for the hint on tinypic.com... I am using it now too. It is just so simple, even simplier than using my own URL FTP program...