I would still say that "the soap attaches the oil to water" isn't quite right. Per your statement, the soap attaches to both oil and water on opposite sides of the molecule, so the oil isn't really attached to the water - at least not directly. That was the thing I was trying to articulate.

Yeah, it's open to interpretation as we aren't utilizing strict scientific terminology. The reason why i preface it that way is that technically emulsifiers are still oils/fats themselves, they've just undergone a chemical reaction that alters their polarity.

Also, when you are trying to create a proper emulsification the majority of the time you add you emulsifiers to the oils/fats first to create a partial emulsification, and then you add your water and energy to finish it off.

But I understand your reasoning, even the best emulsification is still technically an aided dispersion and will lose its homogenisation over time.