Come to think of it, as far as the Olympic movement is concerned, "Great Britain" (i.e., the UK) if a participating nation. They were in the Opening Ceremony parade. England, Sctoland, Wales and N.I. don't exist among Olympics-eligible nations any more than do New York, California, or Louisiana.

So, yeah, it was apparently the decision of the four separate national associations within the UK NOT to unite for Olympics purposes that kept them out.