What would be the opposite of the phrase "Truer words were never spoken" ?
"I am truly grateful", said Alfred. "Untruer words were never spoken", snided Shelly.
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An answer along the same line of thinking as David's answer, but more relevant in American English would be to say "Horse-Shit" or "Bull-Shit". It's used in much the same way that British English uses "bollocks" in that you would say "What a load of Horse-Shit!" or "What a load of Bull-Shit!"
In implementation, it is important to note though that Americans say "shit" in a lot of different contexts. "This is some good shit", "She's got her shit together", "I'm tired of your shit", "I feel like shit", "She's a piece of shit", "She lost her shit with a coworker", "This has turned into a shit show", and "The dog shit on the carpet" all have distinctly different meanings. Shit is so ubiquitous that you can just drop it in a sentence wherever you want and it probably has a relevant meaning. So, it is important to specify "bull" or "horse" when talking about untrue things to avoid confusion.
The exception would be if a person speaks a lot of horse shit, you would say they are "full of shit" in which case you do not need to specify the droppings as those of one of the aforementioned ungulates to know you are talking about falsehoods.
If you want the actual opposite of your sentence, perhaps this would work:
Falser non-words will always be non-spoken.
Your example becomes:
"I am truly grateful", said Alfred. "Falser non-words will always be non-spoken.", snided Shelly.
Fits perfectly with snided, right? Shelly is one clever individual. :-)
Update: As per @Nossjimiki's comment, one might use unspoken in place of non-spoken, in which case the OP's example becomes:
"I am truly grateful", said Alfred. "Falser non-words will always be unspoken.", snided Shelly.