Yes, I agree. And when my kid jumped into a pool he did not actually say he got wet, but I assumed it all the same.
Does 2 Peter 2:1 say the false teacher was purchased? Yes. Does 1 Timothy 2:6 say Christ gave Himself as a ransom for all? Yes. And I am going to say that His purchase was made when He died as a ransom for all, therefore logical necessity requires that
2 Peter 2:1 is referring to being bought with His blood.
And note folks, no alternate view, bought with "something else" has been put forward.