What is the meaning of the phrase, "tight as Dick's hatband"?

That is one I never heard before. I looked it up in my word and phrase origin book and this is what it says. 'The phrase refers to the fact that the crown was too tight for a certain king. The kings identity is unknown but popular theory suggests Oliver Cromwell's son Richard who was nominated by his father and served only 7 months beginning in Sept. 1658. Another person thought to be the mysterious king is Richard III who assumed the throne in 1483. Long regarded the evil king who ordered 'accidental deaths' of his nephews. Richard is said to have been uncomfortable wearing a crown bought with blood. So therefore it was 'tight'. Having never heard this expression before it was interesting to read about it.