The Smith's paper vs the Parkinson's foundation

Question

Following grammar rules I know (quoting):

The ’s is placed immediately after the last letter of the author (or name, country, etc.). Note: do not use the before the name of the author.

..

Do not use the + name of person + ’s.

So according to that, the following example is wrong:

The Simpson’s paper is an excellent introduction to the topic

But why the following works:

The Parkinson's Foundation makes life better for people with Parkinson's disease
The coalition has developed the Parkinson's Disease Composite Scale

I feel the definite article is somehow bound to the "foundation" and "composite scale" words in the examples. But on the other hand, it is before the name (Parkinson) which uses the genitive.

Or in this case, Parkinson's is just understood as the name of the disease and thus it is used as an adjedctive? As in The Clinton foundation (why not Clinton's, then).

Answer 1

The Parkinson's Foundation, according to their website, "makes life better for people with Parkinson’s disease" (emphasis added).

The foundation is not named after a person called Parkinson. It's named after a disease and the name of the disease is Parkinson's disease, not Parkinson disease. If the disease were called Parkinson disease, the organization would be the Parkinson Foundation.

Compare with the Multiple Sclerosis Foundation, which is an organization that works with people who have multiple sclerosis.

Or, for a trickier example, take Lou Gehrig's disease. Lou Gehrig was a famous baseball player who contracted a disease called amyotrophic lateral sclerosis. Lou Gehrig was so famous and the disease was so little known when he got it that the condition came to be known as Lou Gehrig's disease.

The fact that there's a famous person, and a disease named after that person means that hypothetically, there could be a Lou Gehrig Foundation and a Lou Gehrig's Foundation.

The Lou Gehrig Foundation would be set up by Lou Gehrig (like the Clinton Foundation was set up by Bill Clinton and the Gates Foundation was set up by Bill Gates) or set up by someone else in his honor (like the John Birch Society), while the Lou Gehrig's Foundation would be focused on the disease.

As a matter of fact, the Lou Gehrig Society does exist. "The Lou Gehrig Society is dedicated to honoring the legacy of baseball giant Lou Gehrig by offering targeted scholarships and grants that promote public health, wellness and integrity in America."

Answer 2

Or in this case, Parkinson's is just understood as the name of the disease and thus it is used as an adjedctive?

Yes, exactly, “Parkinson’s” is the name of the disease so it is used like an adjective here. The possessive in the name isn’t relevant. “The Cancer Foundation”, “The Diabetes Foundation”, “The Multiple Sclerosis Foundation”, etc. also could all work as names if such organizations existed.

As for “The Clinton Foundation”, “Clinton” is the name of the foundation- it is a family name and it’s common to use “The” + the singular of a family name as an adjective + “foundation”/“organization”/“fund”/etc. when naming something after a family. Note also that this is a family- there is more than one Clinton, so it is not “Clinton’s Foundation”. Though “The Bill Clinton Foundation” would also be an acceptable name in terms of convention. See also “The Obama Foundation” e.g.