How can Bud Lawrence own the rights to the word "frindle", in Frindle?

Everyone knows that Nick made up the word
frindle because he appeared on talk shows saying he
did.

In Frindle, Nick
decides to make up a new word for pen.  He calls it a
frindle.  Nick is only a fifth grader, but his teacher ensures that
the word gets media attention by not giving in and insisting on punishing anyone who
uses the word.  As a result, the word gets popular and kids being using it, and since
they are punished for using it, the adults are soon hearing about
it.

A local newspaper reporter writes about the story, and
soon it goes to regional and then national media outlets.  Soon, people want to buy
things with the word frindle on them.  Bud Lawrence’s lawyer
advises him that the orders are “trouble.”

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The whole country knows that that little kid
made up the word, and unless you make a deal with his dad, you’re going to end up with
nothing—maybe even a big fat lawsuit.  That kid owns that word. (ch 12, p.
78)

As a result, Lawrence
buys the rights to the word from Nick’s dad.  Bud Lawrence gives Nick’s dad a contract
for 30% of the profits, and a check for $2,250 for the amount he has sold
already.