Full bright faces are getting influenced by the environment (EEP) settings when it shouldn't be affected. Specifically from the Brightness/HDR Scale slider and sort of from the Reflection Probe Ambiance. As for how much does the Reflection Probe Ambiance affect Full Bright, the effect is minimal regardless if inside or outside of a Reflection Probe and I wouldn't worry about it too much. Though it does in a way do something "helpful" with Full Bright, which I'll mention later.

As a side note for any reader that might not know, any of the following URL links below that mentions Windlight or URLs about it from your own research - EEP is what "replaced" Windlight. Same with how from what I understand and found out in terminology that Scene Gamma "replaced" Gamma. After that the Brightness/HDR Scale replaced Scene Gamma. Though the only way I've seen the Brightness slider turn into HDR Scale is when Reflection Probe Ambiance at a minimum is 0.01 or higher.

The 1st image URL is a Windlight XML example. The 2nd image is the EEP Personal Lighting menu before PBR. While the last is after PBR was introduced.

The following is an example video of going through the different sky options that have different Brightness/HDR Scale settings. The default is 1.0, but could range above or below that number such as 0.91 or 1.5 and etc. Though you could test with your own Brightness slider levels to see the effect yourself in any sky option. - https://gyazo.com/d496db80fc20f4c77ae0960db3355ea1

The "original" Full Bright - https://wiki.secondlife.com/wiki/PRIM_MATERIAL_LIGHT

How Full Bright is supposed to and expected to work - https://wiki.secondlife.com/wiki/Deferred_Rendering_Test

Now back to the part about the Reflection Probe Ambiance (RPA). From what I tested, the overexposure from Brightness is "mostly" countered when RPA is active (0.01 or higher). Which brings me to an idea of two solutions, that is if possible to do either one. The first idea would be to either give users a checkmark next to Full Bright to set the face Brightness to always 1.0 regardless of whatever the "Sky - Brightness" is set to or to just have Full Bright always set to 1.0 Brightness. The second idea/solution would be to have something similar to RPA applied to the Full Bright face to counter Brightness, but with this you could do what I mentioned earlier and have a checkmark option for it next to Full Bright or when Full Bright is on just have it always applied. Though for either solution, maybe best to just give people a checkmark option to allow a natural transition for those that want it or don't want it.

As for those that might say, well you could just change the Sky EEP or manually set that Sky EEP Brightness down to 1.0 but the problem with that is that it wouldn't exactly be a solution since that would ruin the look of those specific EEPs or parcels/sims in the first place. At least with my maybe possible solutions it gives creators or parcel/sim owners a choice for the creative look they're going for.

Lastly, is it fully possible to do this? I don't know and also depends on how things were scripted. Though with how RPA interacts with Full Bright regardless of a Reflection Probe being there or not, seems to suggest that it might be possible to add something like this to Full Bright to counter Brightness/HDR Scale and it wouldn't hurt to give it a try because of this.