HI, I'm the owner of the Mazda 2, 2011, I bought it at Rosenthal Nissan Mazda of Tysons Corner.

My car has not been full 3 years yet, and I've driven it only for 27,000 miles so far.

Last November, I got my oil change done at the Dealer
(I've got it at dealer always).

and it's been only 3,000 miles since the last oil change.
(As I'm a undergraduate student, I don't drive much)

Last Thursday, while I was driving on 123, a local way,
the Oil-Drain-Plug got popped out
(IT'S NOT BROKEN, BUT JUST POPPED OUT)

So my car start smoking at the bottom and leaking engine-oil.

Then, I immediately parked my car at the mall right next to 123.

Fortunately, there was an auto-shop, so I fixed my car at there, then claimed
my Dealer only just the amount of money that I paid for, believing that the
Oil-Drain-Plug popping out is not my fault.

But, they refused to pay me back, saying that

"It's been 5-months (3,000 miles) since we've changed your oil, if we haven't tighten up the oil-drain-plug well, it would've popped out way sooner than 5 months (3,000 miles), so it's not our fault."

BUT I STILL DON'T GET IT

Can Oil Drain Plug really pop out within 3,000 miles after tighten up correctly?

And is it really my fault because it's been O.K for 3,000 miles?

 

I don't think it is your fault because you personally never touched the oil plug.

On the other hand it will be impossible to prove that it was the dealer's fault.
Lastly: it will be impossible to tell how long it will take for a plug to come loose if it has not been tightened correctly.
It is one of those "stuff happens" things. Let's just hope the engine didn't take damage.
Are you going to go back to that dealer for service?