An excuse can be factually correct and still keep you stuck.

Every detail of an excuse can check out and it will still function as an excuse, because its job is not to be false but to end the inquiry. The traffic really was bad. The timing really is difficult. The accuracy is what makes it effective, since a true reason is harder to argue with and therefore better at keeping you exactly where you are.

Test a reason by asking what you would do if it were true and you still had to move. Usually something small remains available. Do that thing, and let the reason keep being true without letting it be final.