Huh.
First off there is no performance difference between 568A and 568B (Ethernet or HDMI) and while I can not speak for other Mfgr's, we only stipulate 568B in our HDBaseT products because if I don't spec something everybody will call asking which to use.

When this issue first popped up on the forums I searched and read every thing that I could find regarding performance differences between A/B.
While there was always a post saying one was better, there was never an actual reference to hard test data. Jeff B. and I have talked about this a number of times and as best as our testing/research can find (and Jeff has a very well equipped lab) this is all BS and hearsay.

Telling a dealer it is not working because he used "A" instead of "B" is in my opinion right up there with "really, that is the first time that we have ever heard of that problem". Now asking the dealer to re-terminate may in fact solve the problem. Not because of the color code but because hopefully the dealer paid more attention this time.

Now to the real meat of the issue.
568 (anything) is a poor choice for HDMI, the splitting of the pair (orange or green) around the middle sets up some troublesome timing issues. Dealing with those time problems correctly requires complex trace routing inside of a multilayer circuit board (read time/money) that the vast majority of companies will not spring for (Crestron does try to do it right). Note that the multilayer boards (required for HDMI) also create their own problems with impedance that can be mostly mitigated thru the use of VIA's (the small holes thru the circuit board).
The better way to run High Speed Digital Video/Audio (HDMI) over Cat/x is by keeping the pairs together.
First you will maintain a balanced (which HDMI is) and secondly by keeping the pairs together you will minimize the timing errors.

Last and NOT least: The brand/quality of your RJ45 terminals.
People I can not stress enough how important your termination is (regardless of termination color code), this is where the system failure is most likely to occur.
DO NOT use push thru style terminals (the cutting blade stretch's the wire from under the blades reducing bandwidth).
Replace your compression tool Die-Set on a regular basis.
It is recommended that you do not use Ideal brand terminals (there is too much slop).

Remember that the Ethernet Data is redundant (it will keep trying until it gets thru), HDMI data is ONE shot. If it ain't there TFB its over.