Yes, I think Lammy was telling the truth. It's a storm in a teacup. I agree that KS has to be like Caesar's wife when it comes to any hint of cronyism, and I believe that he is a decent and honest man who will do his best to root out any corruption. He's not going to get it right every time.
What I think the government is doing really badly is getting the Comms right. These days, when there is 24 hour news, and people picking up on every tiny thing, it is vital that political parties have someone 'controlling the narrative' as the saying goes. If they have anyone in that role, it's time they were replaced. The WFP debacle was handled very badly, as was the release of prisoners. Both could have been presented very differently, particularly as the LP Comms people will be very aware that the vast majority of the press and media companies are 'unsupportive' (understatement).
I think both were the right thing to do, but the WFP cut should have been announced in the budget, with a phased reduction, so that those just above the PC threshold got a percentage of it, decreasing until it stopped, and anything that the budget holds in mitigation should have been announced at the same time.
Sunak was responsible for the prison crisis. That should have been spelt out more obviously, and information about the types of prisoner and how much of their sentences were outstanding should have been given. There will be dangerous criminals released every day, but as they've served their sentence they have to be set free. All that makes the press is that people have come out of jail, and details of their crime are given, but not that they only had 3 more months (or whatever) to serve.
I'm in no way suggesting that things should be covered up or twisted, but that there should be a more upbeat version of events fed to the media, so that the constant assaults on everything the government does can be countered.