You are right, this does appear to be a bug. Its very strange since the public trade used to be working, and it was introduced in Mys v1.3.4 so nothing should've broken it. I will test the script again later today and let you know the fix I find.
Edit:
Found the fix, it was a glitch. Just one line of code will fix the public trade issue. To do this, go to script file trade.php in your root directory, and locate line 71:
PHP Code:
$validator = $this->trade->getValidator("public");
Change to:
PHP Code:
$validator = $this->trade->getValidator("private");
This should make your public trades work again. As you can see from the code above, when you reply to a public trade offer, you are in fact sending a private trade to the original poster(although your options may be limited, as the poster may specify exactly what he/she wants from a certain adoptable/item type). For this reason, the validator should validate the trade as a private trade, rather than another public trade. Hope this makes sense to you.
Also I've attached trade.php file in this post, you may just download it and replace your own trade.php file through ftp.