Does a tiebreaker contaminate the statistics?

Starting with runners on second and no outs in extra innings
They say the pitcher who comes in gets their stats contaminated,
but isn't this the exact same situation?
A relief pitcher coming in during a regular inning with runners on second and no outs;
the batter enters the same situation regardless.
Even if the pitcher gives up runs in that situation, it's an unearned run,
so it doesn't seem like they lose much.
What exactly is being contaminated?
In baseball, a tie doesn't award points like in soccer,
and in basketball, they play unlimited overtime.
I don't understand the people who oppose this.