Capital gains tax: you invested money and you got a profit
Income tax: the system is based on "Trust". You report xxxxx$ per year, the institution trust you, they won't ask you to prove. But if by any chance they find out you cheated (whatever the method used), they won't forget you, and it is at this moment they will ask you some proofs (taxes control or fiscal control)
When you're working in a manufactory you don't give proofs of your income, right?. It's the same as a freelancer. You can't give them your Skype conversations, emails, etc showing you make an agreement with someone that you don't even know the name. It's the same, it's based on Trust
Also, you can always give your history from an exchange if they ask for proofs, that's why you can download a CSV file on exchanges.
As for the guy on Reddit, any decent bank will freeze or terminate your account when you receive such a big amount
I don't know where you are from, but this is not true. If you are a freelancer, you must sign up in the government and specify what you are doing (for example, if you are making Youtube videos, I think you must sign up as "production of audiovisual content" or something like that) and you must present the receipts that Google pays you through Adsense, and you must also pay some taxes on all of this. I didn't had any idea of all any of this and im learning now. But forget about the concept of "im innocent until proven guilty", you are guilty by default and you must prove that the money you put in your bank account is legit. You may go under the radar for smaller amounts, but any relevant amounts and they will catch you sooner or later and if you don't have everything signed up and ready they will screw you up.