All but one means that in three of the sentences the use of the word base is correct, and in one it is wrong.
However, the statement is wrong, because the verb base can be used, and is used correctly in all those sentences. They can also be put this way:
He bases his arguments firmly on fact.
They base their friendship on mutual respect.
Her novel is based on her family’s history.
He bases his arguments on sound economic theory.
You wrote [size=150]5[/size] sentences/phrases in your first post and I changed 4 of them and used base as a verb. I changed all but one of your sentences/phrases; I changed 4 out of 5 of yours.
Yes, the 4 that I changed are:
His arguments are firmly based on fact.
Their friendship is based on mutual respect.
She based her novel on her family’s history.
His arguments are based on sound economic theory.
These 4 sentences are correct. I wrote them to illustrate how to use base as a verb.
The point here is ‘base’ is advised to be used as a verb while "basis’ as a noun. Then how about if base is used as a noun? Generally, how to use them correctly as nouns.
Thanks a lot.