The phrase "admittedly false" is correct and usable in written English.
It can be used when acknowledging that a statement or claim is not true, often to provide context or to clarify a point.
Example: "While the theory was admittedly false, it sparked a significant amount of debate in the scientific community."
Alternatives: "undeniably incorrect" or "acknowledged as untrue."
Mr. Dutschke and Mr. Curtis had feuded, mostly online, on a variety of topics, including their music careers, Mr. Curtis's admittedly false claim of being a member of Mensa, and Mr. Dutschke's unwillingness to publish the organ-harvesting accusations in a local newsletter.
Responding to Clapper's admittedly false answer to Wyden, seven Republican members of Congress wrote to the attorney general in December seeking a Justice Department investigation into potential perjury.
Some at the network have speculated that former "Nightly News" anchor Tom Brokaw isn't a fan of Williams and has been particularly upset about his successor's admittedly false claim about his Iraq war reporting.
We're angry that our administration, under now-admittedly false pretenses, has caused more than 30,000 deaths; has made our nation less safe rather than more; and has mobilized much of the world community, not just the the Islamic extremists he invokes to frighten us, against us.
Twice as many people still think it is more important to provide needed government services than to hold down the size of government (admittedly, a false choice).
For instance, when Director of the NSA, James Clapper, admittedly gave false answers to Congress about the bulk collection of data, some members of the Intelligence Committee rushed to his defense.
The conclusion of the conditional form is resisted by noticing that some conditional premise fails to be true; though, admittedly, none is false.
There is, admittedly, some risk of false advertising.
What was true in the 80s and even the early 90s largely rings false now (although, admittedly, weekend shopping is still hit and miss).
Admittedly, there's a steep learning curve in applying false eyelashes so that they look natural and stay put.
Men – in theory – are kept out because it requires a Facebook log-in to join the app (admittedly some men may well be driven to create a false Facebook profile just to log in).
