Master of none,

" Reserve the use of the word frozen to something below 32 degrees f."

Not everything freezes below 32 degrees F. That just happens to be the freezing point of water.
Anything that is solid is technically frozen. Think about a chocolate chip - it is a solid, but it melts when it is left in the sun right? So, if something can melt (which all solids can) then it must be able to be frozen too. (freezing and melting happen at the same temperature for each object, it just depends if you are cooling it down or heating it up)
Although it doesn't fit with how we view the world, scientifically speaking, she is correct. (Sorry to say this, as it sounds like this drives you crazy.)
We had a similar issue with our DD6 a while back, luckily she got out of the phase before it drove me too crazy. (Of course she's now onto a different equally frustrating phase)