Like hell.
I had a personal visit from an officer of the DOA who showed me his badge and told me in advance that, if he found out that I had lied during the interview, I could end up in prison.
In my day (before the Church Committee), for a TSCW, it was personal FBI interviews of almost everybody I had ever known (no phone calls - too inscure), plus background checks on them, together with school and police records. Followed by nearly a year wait while the data was analyzed, followed by a year's ‘probation’. Not to mention the 10 year prison, $10K fine - minimums - for anything I divulged which was considered classified - including newspaper stories.
DOA investigators were not in the picture then; they were considered too lax. I doubt they are any more rigiorous today.
You might have gone to prison for lying, but you did not apparently sign anything; I did and would have gone - no questions asked - to prison.