I think you also forgot to mention the part of telling them that you're recording the discussion and that they agree to it. I say that because it is different today with mobile phones, as people don't put this little cassette recorder down on the table, and instead use their mobile. Just about everyone has a mobile, so putting it out does not tell the person they're recording the conversation.
I have read cases where what you describe are tossed out because the person still didn't know they're being recorded, which breaches their privacy.
I am not making a point about this to argue, but you are giving advice publicly on this website to someone which could be telling them to do something against the law, which is why I am clarifying what's legal in most western countries when it comes to recording a conversation.
This is why when such conversations are recorded by companies via support and such, they must legally tell you, i.e. for training purposes, AND give you the option to not have your conversation recorded but to still receive technical support.
Privacy is privacy nowadays, and privacy laws are very strict. You're actually breaching a persons privacy if you take a picture of something on your phone that has them in it, then publicise that photo online. That breaches their privacy by law in most countries. You need their consent if you wish to publish the photo online, for example, more often than not.
Privacy is my key point here... and unfortunately you can't take your mobile out of your pocket and start recording a conversation with someone without telling them, as that is breaching their privacy. Informed consent is part and parcel of privacy, by law. Entrapment comes to mind.