I do like this theory, and I believe both ways can happen, honestly, I am on the fence. There will be manga spoilers in this. you have been warned

To start this off, I am going to say why I believe this might not work. 

The doctor was right. All quirkless children have that extra joint.

Quirklessness might run in an undiscussed part of the family

He was not born quirkless, but it was not stolen (If you want me to go more in-depth with this idea, let me know)

Now, the reasons it might be true.

The doctor that treated Izuku is the one that treated all for one. The doctor might not have stolen the quirk, but he could have hidden it up.

Honestly, that's it for now. I love how this theory evolves and I might even add more to either reason.

Tell me if you like me looking at how both sides could be true, or just give my opinion and have everyone discuss it. Like I said the last chapter, I would love to read your ideas on this theory and why it could go one way or another