Yeah, it's real.

It would usually happen when both parties already have their weapons drawn and ready and they have surprised one another. After all, if you have the drop on your opposition and you are willing to shoot, why would you let them get into a potential position of advantage?

What would "normally" occur is that one group or the other would back away slowly to end the confrontation. This is because these types of situations can easily end with everyone getting shot and that's rarely seen as being a tactical nor a strategic advantage. The groups may re-engage later (even within minutes of the standoff itself) . However, the standoff is almost always an unpleasant surprise for all involved and its nonviolent resolution is seen as being paramount.

You rarely hear about Mexican standoffs as if things go wrong, many of those involved are injured or killed. There's also the fact that whatever it took to end the standoff may not be a type of behavior that the tellers of a story want promulgated about themselves and their personal bravery.