Meaning of words
If another party, perhaps located in Cheltenham, has access to the records database then "UKSA won't volunteer to disclose the info" is correct under all data snaffling circs.
The statement that matters needs to say "No party outside ONS has access to the census data" and then enumerate exactly what products are generated fom the data.
Remember that the US census was supposed to be secret too, but was used to identify Japanese-Americans in WW2.
The question I'd like to tack on would be "If we find out that you lied, what would happen to you?".