The background parentKey is in the xml file for the lua file you linked, just in case you missed it ..
Code:
<Button name="CompactUnitFrameTemplate" frameStrata="LOW" inherits="SecureUnitButtonTemplate" virtual="true">
<Layers>
<Layer level="BACKGROUND">
<Texture name="$parentBackground" parentKey="background" setAllPoints="true" ignoreParentAlpha="true"/>
</Layer>
<Layer level="BORDER" textureSubLevel="5">
<Texture name="$parentMyHealPrediction" parentKey="myHealPrediction"/>
<Texture name="$parentOtherHealPrediction" parentKey="otherHealPrediction"/>
<Texture name="$parentTotalAbsorb" parentKey="totalAbsorb"/>
</Layer>