It's hard to tell if it was a theory or an aspiration...
Bradley Wiggins has said that seeing Chris Boardman was the 'inspiration for taking up cycling when he was 12'
Other successful athletes have said similar.
That sort of evidence may well have been used to justify more large scale sporting events.
Extrapolating that to say 'and it will inspire the general public to exercise' may well have been used by sports organisations looking for (government) money.
Whether Govs were gullible, conned or just wanting it to be true so they didn't have to take tough decisions is an open question.