What resolution are all the displays?
Short answer, it does work. Not sure why you had trouble.
Apple Mini DisplayPort adapters: Frequently asked questions (FAQ)
http://support.apple.com/kb/HT3382
Guide to Apple graphic display adapters needed
https://support.apple.com/kb/HT3235
Atlona (Dual Link) DVI to Mini DisplayPort Converter for Apple 27-inch LED and 27-inch iMac
http://www.atlona.com/Atlona-Dual-Link-DVI-to-Mini-DisplayPort-Converter-USB-Pow ered.html
Mac Pro (Early 2009), Mac Pro (Mid 2010), Mac Pro (Mid 2012): Issues with three displays and multiple DVI, HDMI connections
It's not the USB data that is needed to run three displays. It's the extra POWER. If you read the Apple article, they say the only solution they endorse is their US$100 Dual-Link adapters. Check the table at the end of the article.
Mac Pro (Early 2009), Mac Pro (Mid 2010): Supported display configurations
Readers here have found that if you have two Brand-X Powered adapters, aka active adapters, it also works fine. These do not always require another USB. If designed recently, they can pick up a power pin in the Mini DisplayPort interface.
AMD (makers of the 5770 and 5870) lists the qualified POWERED adapters that meet their most stringent requirements. Look down the page and you will find several qualified Active Mini DisplyPort to various others, such as HDMI. These adapters are available from other outlets, such as Amazon, sometimes for far less than the Apple adapters.
http://support.amd.com/us/eyefinity/Pages/eyefinity-dongles.aspx
The other desktop monitor will plug directly into the DVI port on the card and the 40 inch tv will still connect via HDMI over the second Mini Display port.
That will work only if you use an active Mini DisplayPort to HDMI adapter.
The only (someone) have found to work (2009)
http://www.alibaba.com/product-gs/337561577/miniactive_display_port_tohdmi.html
If you want audio via HDMI, you can use audio from the Mac Pro's optical output with this DVI to HDMI converter:
Print out the above and send it to that rep when you get yours working perhaps?