"An argument is valid IFF the premises are false or the conclusion is true".
misses an important feature in the textbook's definition. Namely, you've lost the must, but the must is crucial.
The validity of an argument does not hinge on the truth or falisty of its premises or the truth of its conclusion. Instead, validity looks at the sum of all of the operations and rules of inference in an argument and evaluates it in light of every possible condition of the truth and falsity of every premise and the conclusion.
E.g., consider the following two arguments:
(1) If the moon is made of cheese, Kaguyahime lives there.
(2) The moon is made of cheese.
Therefore Kaguyahime lives there.
This argument is valid on your definition (at least one false premise). And valid on the must definition -- if the premises are true, then the conclusion must be true.
(1) The moon is smaller than the sun
(2) The moon is not made of cheese
Therefore, Apollo 11 went to the moon
This argument is valid according to your definition -- it has a true conclusion. But it is not a valid argument on the textbook definition. Why? Because there is an imaginable set of the variables where the premises are true and the conclusion is not (it is not the case that the conclusion must be true if the premises are true).
Argument 2 can be rewritten:
Per the fundamental rules of logic, S can be either T or F, C can be T or F, A can be T or F. This gives us 2^3 (8) possible arrangements of these variables. And one of these is this: S is true, C is true, and A is false. This breaks the must
Thus, your sentence is not an accurate articulation of validity because you've lost the modal consideration.