Got busted for pushing motorbike without helmet. How fair is that?

Definitely wouldn’t have a strong defence. Interestingly the first case I ever witnessed (as a sixth former) was essentially this. A man walked back home drunk from the pub and arrived home later than he told his wife. His wife told him off. He argued and his neighbours overheard the arguing and called the police. In the meantime the husband walks out (or is kicked out - I can’t really remember) and walks down the street to his van where he goes to sleep (not really a campervan per se, some sort of transit type van with a mattress in back). The police arrive and start investigating. The police go to his van and wake him up. The man is arrested and charged with being drunk in charge. He pleads not guilty at the early administrative hearing and goes to trial at the Magistrate’s Court (the case I saw). He essentially argued necessity and that he had to sleep in the van to prevent the situation worsening and to prevent conflict. Bizarrely, at trial, his wife admitted that she was very angry and acted unreasonably (he was a builder of some sort so they both needed him to keep his driving licence). The District Judge found him guilty. I didn’t see the sentencing but I can bet he lost his licence. I’ll always remember what I thought was horrific injustice and it was probably the leading factor that made me go into the law (not that I’ve ever done any criminal work since). But unfortunately (and imo wrongly), in the circumstances you described, they’d have no defence.