History Lesson Anyone ?

[Chess Ref]

I am hoping to get a historical context of the two base award "at the time of the pitch."
I am in my third year so my references only go back that far.

I had this Sitch or something very similar happen 3x times this week with 3 different partners.

Runner on 1B. Basehit to RF. Play on Runner @ 3rd Base. Lets assume BR is between 1B &2B by now. Ball is overthrown into dead ball area. I say BR should get 3B.

I have all 3 partners bring out the "at the time of the pitch" card when we have had discussions on where to place the batter runner.

I say BR should get 3B. Am I totally screwing the pooch here ? All 3 partners say no "time of pitch yada yada yada.....

What say you ?