If The Judge is correct, they've missed the bigger issue.
If Williams only found out about the problem when building the car last week, that means that as of last week, the car wasn't built yet.
You can't send a car to be crash-tested until it is built.
You can't test a car until it passes the crash test, and said test lasts an entire week, Monday-Friday, not modifiable by the teams. (It's possible under The Judge's theory those lorries could be off to Paris for that testing but there would be no point taking them to Barcelona without stopping off there first).
Therefore, if this is the reason, Williams can't possibly participate in this test, because the earliest they could pass the crash test is next Friday (i.e. just in time for the second test). If they want any testing at all, they must pass that test, so they'll need to be conservative regarding how the car is, but that's relatively minor at this point - on this theory, they're guaranteed to miss 50% of testing. And they're worried enough not to admit this upfront, suggesting something large (such as sponsor money) is riding on how said non-participation is handled... ...which could lead to a heavy price down the road due to burning up that amount of goodwill advertising. Note that the first test is televised this year, but the second probably is not.