Actually that case might be caught, depending on the architecture. E.g. on RISC-V float and integer registers are separate and the compiler would fail if you tell it you want an integer register and you try to load that with a float.
That's his "aha, they are typed!" gotcha, but it's really not what anyone was talking about. And anyway, even in that case it isn't guaranteed - RISC-V has an optional configuration where float and integer registers are the same.