What is a Riven Word™ / Phrase™?

_{This is in the spirit of the What is a Word/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles.}

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If a word conforms to a special rule, I call it a Riven Word™ or Phrase™.

Use the examples below to find the rule.

$$\begin{array}{|c|c|}\hline \textbf{RIVEN™} & \textbf{UN-RIVEN™}\\\hline \text{ROBE} & \text{COAT}\\\hline \text{AMZN} & \text{MSFT}\\\hline \text{GNAT} & \text{WASP}\\\hline \text{THUG} & \text{RUFFIAN}\\\hline \text{RAVINE} & \text{CREVICE}\\\hline \text{ANGER TAN} & \text{RAGE BURN}\\\hline \text{LIAR ENVY} & \text{TRUE LOVE}\\\hline \text{RINSER FAVE} & \text{AERIE CHURN}\\\hline \text{GENTRY LEG ART} & \text{COMMON ARM TAT}\\\hline \text{RAVER TANGERINE} & \text{RESERVED ORANGE}\\\hline \end{array}$$

CSV version:

RIVEN™,UN-RIVEN™
ROBE,COAT
AMZN,MSFT
GNAT,WASP
THUG,RUFFIAN
RAVINE,CREVICE

ANGER TAN,RAGE BURN
LIAR ENVY,TRUE LOVE
RINSER FAVE, AERIE CHURN
GENTRY LEG ART,COMMON ARM TAT
RAVER TANGERINE,RESERVED ORANGE

Answer

First off, if you're reading this, please upvote TwoBitOperation's answer - he did a lot of legwork on this one that made me see the answer.

A Riven word can be defined as:

Any word or phrase which, when ROT13'ed, the result is the same word or phrase, but backwards

Examples:

ROBE = EBOR
... but COAT = PBNG

AMZN = NZMA
... but MSFT = ZFSG

RINSER FAVE = EVAFRE SNIR
... but AERIE CHURN = NREVR PUHEA

RAVER TANGERINE = ENIRE GNATREVAR
... but RESERVED ORANGE = ERFREIRQ BENATR

The reason that each of these words is called a Riven word/phrase is

That "A RIVEN" itself is a Riven phrase:
A RIVEN = N EVIRA