I honestly think you're misreading the tone of those comments and looking for something to be offended about Haworthia.
Speculating about whether someone has a nanny is just idle chit chat - prompted by awe that, if they don't, they either have extremely chilled children, an extremely well-organised routine, or both.
One of the comments you quote was mine and it wasn't the least bit snide or snobbish, nor was it a 'complaint'. Children are not impressed by tabloid coverage or by grown-ups talking about themselves - fact. That part of the session bored my DC, who had no idea what 'being papped' means and just wanted to get on with the exercises, quiz and shout outs (and love seeing the chiildren - we loved King Arthur and Zog on Friday!).
What I have said, with great enthusiasm on another thread though, is that those little 'slip ups', also including pop-culture references that aren't really age-appropriate (like The Office and some cultural figures referenced in quizzes), are part of what makes the whole thing so engaging - precisely because Joe clearly isn't a 'proper teacher', he's more like a 'fun uncle'. If he was too prepared, earnest and perfect, kids would get bored.
Because you know, having to get things just so, to every viewer's taste and spend time earnestly explaining things to naysayers, just in case someone gets the wrong end of the stick... it kind of kills the mood and the flow, don't you think?