OK "invalid" may not be the correct term, would you prefer "unresolved"? certainly the synonymy isn't universal around the world.
I have always failed to understand how 2 different plants can have 2 different names which are considered synonyms.
B. alba var. rubra could be a synonym of B. rubra, but B. alba = B. rubra ????
The ARS GRIN database used to have many of those, years ago. Today they have a more logical approach (except in this case).
If I am wrong, so be it, I'll plead guilty to being an "ignoramus", I am certainly not a taxonomist.
My problem is matching common names with 2 different bot. names considered synonyms. One ends up with contradictory names which cannot be synonyms since they mean different things... like "Red-stemmed vine spinach" vs "White-stemmed vine spinach". Names with similar meaning exist in French, German, Spanish etc. for both. My approach is to find a bot. name that suits the horticultural rules.
Basella alba L. 'Rubra' for all the names referring to the colour red appears logical to me.
Looking quickly at my favourite references:
GRIN has B. alba = B. rubra
Flora Europaea ignored B. rubra
Flora of China considered both as different species, and so do many of the Indian scholars.