The Danish Embassy actually checks and verifies that it's true. It is not possible to lie about. It's not just a sworn statement. I don't know the process of each individual country's embassy in Thailand, but the reason why immigration wouldn't accept them from for example the US embassy is just that. No check of anything. Just a sworn statement where you could be lying.
or choose another visa option. The new DTV looks promising for example. Elite visa will get you up to 20 years hassle free if money up front isn't a concern. LTR 10 year visa too.
yes, several years ago If from the US your only option is to bank 800K to start with. Then later you can switch to using transfers of minimum 65K into Thailand each and every month.