How come this non-standard ethernet wiring works?
It may depend on your definition of "works".  Ethernet is an AC coupled communications link, so a wire that is mis-connected may still have enough capacitance to the other end of the link to enable data to come across.  

Modern PHY (basically the cable modem) devices have pretty sophisticated techniques to compensate for cable variance.  In some cases you may find that the actual speed of the link has dropped below standard rates because of that during the equalization and training phases of link establishment.  That's why you also have more expensive testers that actually check the cabling the way an Ethernet PHY would use it.  

For example the low cost DC type checkers wouldn't be able to tell that the internal wall cable connections were wired to RJ-61 standards, which would be problematic for Ethernet, but would pass continuity/short circuit tests.  That's not a put-down, they're generally all most people will ever need, but then there are systems where a 50% drop in data rates would be unacceptable (data centers, medical imaging, etc.) and that's where you need the higher end stuff.

Best advice I can give is take the wall sockets off and inspect the wiring there, you may find a poor punchdown connection, RJ-61 wiring, or something else.