Yes, anyone who is female (or wraps up in sufficiently mysterious shawls) and old enough could pretend to be a mysterious old lady, but the actual category of the creatures is a different matter, and one can often tell (though it's better to be on the safe side, when identifying them).
Mysterious old ladies can, in a certain sense, do magic - or help you do magic. Sure, if you decide to take the first milking of your new cow and leave it out in a bowl in the backyard with a garland of roses floating on the surface and then drink it all first thing in the morning without stopping to put on your shoes or comb your hair, nothing will happen. But if you do it because a mysterious old lady told you to, and it was a real mysterious old lady, and you followed all of her instructions? Then you will find that you will get whatever result she advertised.
But if you step into your slippers first or tug a knot out of your ponytail or drink the milk early or late or use daisies for the garland, you will get something else.
It's very important to be exact and careful about these things.
Compared to what happens if you disobey a real mysterious old lady, being occasionally made a fool of by some pretender to the title because your eyesight is going or you were too sleepy to note her lack of a proper mysterious aura is nothing.
"Well, whether or not there's magic involved, the problem will go away when he dies. And people do that."
"No. You can go outside and be conspicuously dismayed about it if you want, but it might not work if you just vaguely heard about the problem and aren't one of the people having it. And it's not a problem I want you to have."
"Well, maybe you can go outside and sigh about that if you can follow instructions to the letter, but in the meantime you need a name."
"I'm not sure. What have you been doing with yourself in the time you've spent doing things other than eating maidens, did you hear any names you liked?"
"I wandered around and hunted animals and swam a lot. I like swimming. When I got lonely I snuck close to villages and listened to people doing things, but then usually they found me and chased me off. I don't remember any names."
"Well, I suppose you could ask one of your parents to name you but I'd understand if under the circumstances it was unappealing."
"Taphinieu says all my magic problems are because of the queen's mistakes and the king is the one who made all those people marry me. I don't think I'm going to like them much."
"Yeah. I could pick something but I haven't exactly given it much thought. Taphinieu, any ideas?"