To pick-up or not is a difficult question, and the answer highly subjective.
Our new boy Barnaby when scared behaves like LG's Henry. Laying down and being submissive. If a large aggressive dog were to attack him in this situation, I feel he'd be badly hurt. So at the moment I'd pick him up.
Our Old girl Betty, became wise to the ways of aggressive dogs, and for her the tactic that worked was different. Always on spotting other dogs with their owners, we'd clip her on-lead. If dogs approached off-lead, and we had the slightest concerns over their intentions, we immediately unclipped her. The reason was that in serious attack situations she always proved more agile than her attackers and quite easily out manoeuvred them. Se was never aggressive, totally avoiding both conflict and biting from the aggressors.
We hope Barnaby will wise up before something bad happens to him.