I'm shocked at the 'suggestion' that he deliberately cheated. = The very 'suggestion' that he deliberately cheated is shocking (to me).
They were careful to avoid any 'suggestion' of impropriety. [=avoid doing anything that could be seen as improper]
There was some 'suggestion' of swelling around his ankle. [=his ankle appeared to be slightly swollen]
(..) It has been six months now and it will expire in days. Why should we lose this opportunity? You don't want to lose this opportunity, then make a suggestion. You know my situation. Tell us what to do, your honour. - His father is his excuse... - He is not my excuse. He's the reason. - Let me speak. (..)2011 A Separation