Tom said If he were me, he would go home

[Thuytrang3004]

Hi everyone,
I am Trang Nguyen, I'm from Vietnam.
I have a trouble with the reported speech. That is:
In the sentence: "If I were you, I would go home", Tom said
The roported speech of that sentence is: Tom said If he were me, he would go home.
I think the sentence: "If I were you, I would go home", Tom said tell about a really impossible thing, so when we change it into roported speech it must be: Tom said If he had been me, he would have gone home (the third conditional setence).
Please explain for me.
Thanks in advance! :P

[Diverhank]

I think "would have gone home" is grammatically correct. However, in daily conversation, most ( native) people would use "I would go home"