Kurds have been crossing the border into Syria predominately from Turkey in waves since the 19th century. Rather than rejecting them they have been welcomed and treated fairly and even given rights like their Syrian counterparts.
“President Assad issued a decree granting Arab Syrian citizenship to people registered as foreigners in the (governorate of Hassake),” said the SANA news agency. The measure, which benefited about 300,000 Kurds, came a week after Assad tasked a committee with “resolving the problem of the 1962 census in the governorate of Hassake.”
In 1962 a census was done which determined that a number of Kurds had incorrectly registered themselves and their children in order to gain Syrian citizenship. 40,000 Kurds lost their Syrian citizenship as a result. Prior to that I believe (I would need to look back to confirm because I am going off of memory from reading hundreds of pages of information on this topic) they did not have an issue.
So basically 40,000 lost their citizenship in 1962 but 300,000 more were awarded citizenship in 2012. That would appear to be a very good compromise, and that's not to say that others didn't have citizenship.. they did but some lost it due to errors or false information they provided.
Think of it this way, if you seek refuge in the United States and during your application you give false information and then the department of homeland security or immigration realizes this.. what happens to you? Most likely you would be deported and your paperwork would be null and void correct? Well Syria did not take these harsh measures but instead allowed them to continue to reside and to live much like their Syrian counterparts.
As far as why it says Arab.. I am not exactly sure but it could have to do with the name of the country being the Syrian Arab Republic.. now does that mean that Aramean's who are Christian were treated differently because they were not technically Arab? No, not at all. In fact Syria is the only country in the Near/Middle East that is secular and nonsectarian.