(I knew that only genesis block reward cannot be spent)
Not only.
I believe there are two cases in the block chain where coinbase TX had the same ID as another one before it.
It is not possible anymore, but it used to be possible.
The two rewards became unspendable when the nodes' implementation switched to LevelDB (that replaced BerkeleyDB for storing UTXO set).
They were spendable before, but now such is the "consensus".
But I don't know anything about "[reward from] the block immediately following every halving can never be spent"
That would be something new, would have to be some implementation bug.
But more likely it's just fake news