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You are correct. If anything in game is the correct ping, that would be the one you see yourself.

However, in order to compare yours to other's pings it is often easier to divide your own by 4 instead of multiplying everyone else's by 4.

Furthermore, there are instances when your ping is NOT correct. This usually happens when your connection is really bad or you're playing from all the way across the world. That is, if you real ping is over 250 (others see it as 62+ I guess).
What happens then is you see your own ping go from 1 to 250 and back.

So all in all, you are right, that is the correct ping, but for comparison using the one others see is easier and there may be instances when your own ping is not correct.

However, in order to compare yours to other's pings it is often easier to divide your own by 4 instead of multiplying everyone else's by 4.

Furthermore, there are instances when your ping is NOT correct. This usually happens when your connection is really bad or you're playing from all the way across the world. That is, if you real ping is over 250 (others see it as 62+ I guess).
What happens then is you see your own ping go from 1 to 250 and back.

Wrong teddy, that was discussed several times on official forums.
Let's imagine, your my neighbor, same ISP and all, i see myself on server with 80 ping and see you with 20 ping. Believe me, your real ping isn't 20, so, i need to multiple the ping i see you by 4 to get your correct ping: 80

When you're having connection issues you see your ping going crazy till 250, come lower and start going up again while others just see you with 250.

And no, when my ping goes above 250, others can still see the ping. Trust me, it's happened to me several times. I see the ping going haywire while others see it as 116 for example.

this.

Sometimes my ping shows 10, while I'm lagging like a b!tch, other see something as 100. Asking for ping is my way of socializing

I used to just tell people to check it themselves using statfps because it does get annoying sometimes checking it for other people.  However, I've noticed that statfps and the scoreboard sometimes shows different results.