Its a region not a people or government there was no Palestinian people
The bedouin nomads have never had a state or government, yet are considered a distinct ethnicity, even if they are spread all over the Middle East.
Just as another example: Prior to the 16th century, 'American' was generally used to refer to the native Indian population. It wasn't until the 17th century that European settlers began to adopt the term as a common descriptor; shortly after our own independence, 'American' came to be the common demonym for citizens of the United States, and the native Indians were no longer commonly called 'Americans' anymore; referring to Americans by the European origin (whether British, French, etc) was discouraged.
The lesson is that nationalist fervor can emerge in a relatively short time, especially if the pressure is high enough: given that the various Palestinians have been 'de facto' treated as a separate class of people by both Israel and the other Arab/Islamic states surrounding them, are you shocked that they would adopt the demonym?