If a UK citizen was arrested on suspicion of a serious offence against property 30 years ago, tried, and acquitted, then they should answer "yes" when they apply for a US visa and are asked whether they have been arrested or convicted. But how can they provide confirmation of their criminal record when they haven't actually got a criminal record?
Note: the US visa application form DS-160 asks "Have you ever been arrested or convicted for any offense or crime, even though subject of a pardon, amnesty or similar action?". But it makes no reference to acquittal, which is not similar to a pardon or amnesty, because acquitted people are recognised to be innocent, whereas those who are pardoned or amnestied are not.
Furthermore, if you answer "yes" to that question, you are asked to fill in a VCU1. The authors of that form too seem oblivious to the possibility that a defendant might be acquitted, since they ask people who have been arrested or convicted of an offence to state what their "sentence" was. If you are convicted then of course you will be given a sentence. But if you are found to be not guilty than that means legally you are innocent, just as innocent as if you had never been arrested in the first place - indeed, just as innocent as all the billions of people in the world who weren't arrested for the offence - and of course you are not given a sentence.
I should add that the ACPO certificate to which the VCU1 refers is a British police certificate specifically meant for people who are applying for visas to travel to foreign countries. That certificate lists only information regarding a person's criminal record. In other words, it lists details regarding their convictions in court and it also lists other official actions which have taken place if the person has admitted guilt but no trial has taken place - actions such as reprimands, cautions and warnings. It does not say "this person was arrested by the police on suspicion of committing crime X, they denied committing it, they were tried by a court, and the court agreed with the person that they did not commit it". It does not contain any information regarding such offences.