This is a bit vague tbh.. mate. Messed around how? Are they asserting that he's missed some objectives they set? Are they claiming they claiming he was due to carry out some tasks/meet some other objectives he's saying he was unaware of? Are they changing objectives continually? I guess the latter is something he'd need to suck up so long as they can acknowledge prior work and that objectives were changed after he'd be working on other things or towards different goals.
Are these annual, monthly or weekly meetings?
Annual objectives ought to be put in writing for sure, I can certainly see a weekly or monthly meeting not necessarily having minutes/notes though and just being a brief thing.
Openly recording could come off as a bit weird and discretely recording is the sort of thing people might do in advance of a tribunal, by all means if he can do it totally discretely and as a personal record do it but I'd not advertise the fact.
One thing he might consider doing, rather than just emailing a meeting summary, is just to drop a weekly update e-mail to his manager say each Friday, just a brief few lines or bullet points checking off his progress on whatever things he's working on, and maybe the odd comment about stuff the manager needs to chase perhaps [X still outstanding, still waiting for Y from Z team, have chased are you able to escalate?] etc.. and then in the bottom part of the email perhaps mention the objectives and which are met, in progress, ongoing etc...
That might help solve his issues, just being visibly productive if there are issues between him and the manager - does the manager know what he's been doing day to day? Like say these objectives are monthly and he's updating this weekly email and showing progress towards them then at the next month the manager is like "oh what about issues B and C" well he's sent 4 emails during the past month showing exactly what he's been working on with the objectives at the bottom and maybe [completed] and [in progress] , [to be done] etc.. next to the objectives and the manager hasn't said anything by then??? Perhaps that regular email then means that sort of thing would be less likely for that to happen - even if the manager is disorganised and this new task/objective comes in mid-month and he forgets he's not told your mate about it.. well they've got this regular email now and they can both refer back to it at the next 1 to 1 meeting. And before that meeting, the manager may well see on one of the emails that matey isn't working on the thing he's going to ask about next week and then realise he's unaware of it and mention it to him.