Simply "false premise".

Similar to @ZachP's Latin phrase a falsis principiis proficisci.

Update (for all the down-voters who didn't care to comment):

A "false premise" is an incorrect proposition that forms the basis of an argument. Since the premise is not correct, the conclusion drawn may be in error. However, the logical validity of an argument is a function of its internal consistency, not the truth value of its premises.

False premises are the underpinning of cognitive biases; although, not all false premises are used to construct a cognitive biases. As an example in the OP's context, "The group's choice to continually cling to this false premise led to the acceptance of an entire web of falsehoods."

Simply "false premise".

Similar to @ZachP's Latin phrase a falsis principiis proficisci.

Update (for all the down-voters who didn't care to comment):

A "false premise" is an incorrect proposition that forms the basis of an argument. Since the premise is not correct, the conclusion drawn may be in error. However, the logical validity of an argument is a function of its internal consistency, not the truth value of its premises.

False premises are the underpinning of cognitive biases; although, not all false premises are used to construct a cognitive bias. As an example in the OP's context, "The group's choice to continually cling to this false premise led to the acceptance of an entire web of falsehoods."

Simply "false premise".

Similar to @ZachP's Latin phrase a falsis principiis proficisci.

Simply "false premise".

Similar to @ZachP's Latin phrase a falsis principiis proficisci.

Update (for all the down-voters who didn't care to comment):

A "false premise" is an incorrect proposition that forms the basis of an argument. Since the premise is not correct, the conclusion drawn may be in error. However, the logical validity of an argument is a function of its internal consistency, not the truth value of its premises.

False premises are the underpinning of cognitive biases; although, not all false premises are used to construct a cognitive biases. As an example in the OP's context, "The group's choice to continually cling to this false premise led to the acceptance of an entire web of falsehoods."