While this may be true, it is odd that the machine appears to attempt to load the hardware test (it goes through all the correct motions before bringing us to the -3404D error). Further, why not simply give a message like, "Sorry, hardware test via the internet is not supported on this Mac," rather than some unhelpful, cryptic message?
Finally, determining if your computer supports loading Apple Hardware Diagnostics over the internet isn't necessarily easy to do using the info from Apple. Quoted from their webpage, "Some Macintosh computers that shipped with OS X Lion and later support the use of Apple Hardware Test over the Internet. These computers will start up to an Internet-based version of AHT if the hard drive does not contain AHT."
Some? How helpful is that? Why don't we throw in "may" and "possibly" and how about "we don't really know" for good measure.
I have an early 2011 MBP 13 that does do the AHT over the internet, and a Mid 2010 that doesn't, so for the 13s that appears to be the cutoff. How hard was that, Apple? FFS