Are Access Data 0 & Data 1 Wires Interchangeable?

4 Wires are commonly used for access readers:

• Red: + voltage
• Black: - voltage
• Green: Data 1
• White: Data 0

But other colors may be used to control the LED, tie a tamper alarm, and so on.

It sounds like you got a handle on that, but I don't follow your written problem. What are 'the wires coming to the reader' if they aren't the ones coming from the board?

Also, troubleshooting a low-level wiring issue before checking the logs is leaving out a big piece of the puzzle. I'd elect to go that route first before getting in the weeds.  

This is a telephone entry system/Call box. Call box is on one island, resident card reader on another island.

Green/White leaves the call box as green/white but enters the card reader enclosure as two other colors. There is a splice somewhere where the wiring changed. Not a big deal, I just dont know which is which. It is easy enough to tone them and sort it out and I will do that today.

But since the problem is so intermittent, and only seems to affect specific cards, I was wondering if this may even be the issue

Well I can not confirm if that would have worked. We toned/metered the wires and had it right first time

The cards that were failing were not in the system. oddly enough the log did not record that it denied any cards. There is no record of those cards being swiped. Is that normal?

The real issue was they could not communicate with the callbox from their PC, so as they created new cards, they weren't at the callbox. Fixed that, and all seems to be good now.

If the reader is wiegand then you will get invalid card reads. You are swapping all of the 1's and 0's in the card read data. A pulse on Data 0 represents a 0 bit and vice versa.