Did she have the right to say this?

I was at a store with my friend(we're both teen guys) he's really into the game minecraft so we were looking around for things related to it. Anyway he saw some minecraft shirts and started looking at them this kid came up to us and said
Kid: Hey dude (looked at my friend) I see that you like minecraft me too
Friend: Yeah I love this game it's alot of fun
Kid: I'm 10 years old

His mom came over and said this
Kids mom: Get over here right now( kids name) you do not need to be talking to perverts who are twice your age
My friend doesn't look old he is just tall for our age(he was wearing a beanie and it kind of covered his eyes but just a little bit) I walked over to the mom and said
Me: You don't need to be calling my friend a pervert he isn't and your son started talking to him about a video game
Kids mom: Wow really do I need to call security on your pervert friend?
Me: I just told you my friend is not a pervert what makes you want to call strangers that?
Kids mom: That is it I'm calling them

I'm not making this up this happened when we were at a store. She said those things really loud like she was yelling and security did come but they didn't tell us anything(because we did nothing wrong) did she have the right to call my friend that?

BQ: Did I do the right thing?

Unfortunately, you'll come across trash like this woman throughout your entire life.
Personally, I like to look at someone like this as though they've just stepped in dog poo. Look them straight in the eye, make a "you're disgusting" face and then walk away.

There was nothing you could have done but explain to security about the situation. You did the right thing by speaking up for your friend, that takes a lot of courage, and you also managed the situation very well with a leveled head. You tried to mend things but she blew everything out of proportion. None of this is y'all's fault, so don't sweat it.
In the future if this type of thing happens again just calmly report the situation, and offer to call authorities yourself. Most of the times the accuser will back down.

Maybe she saw your friend looking to her kid in a different way or something.

Yes, you stood up to her - she was being totally unreasonable.

I think it was good of you to speak up for your friend- letting her know you were both teens too may of made her think twice about speaking in that manner about strangers. If security would of been called they would of looked at her like the trouble maker.
Did she have a right to say it - yes. Was she right? NO

Uh, why are you asking this idiotic question?

Of course she was 100% wrong for insulting a completely innocent person. What is it you don't understand here?

She had no right and good for you for saying something. Unfortunately there are terrible things out there so everyone's suspicious.

Did she have the "right" to say that? Yes.
Should she have said it? No.