Right of Return is one grandparent of either side...which is Israeli law and open to non jews, obviously.
Yes, the idea was to allow a very liberal definition of "who is a Jew" to allow those living Jewish lives and facing persecution for it to enter Israel. The net result has been to let in a lot of (about 250,000) non-Jews. IMHO, it is greatly abused by people who are not Zionists, who do not really identify as Jews, and who don't really belong in the country. They had to claim to be Jewish and to have a rabbi sign a letter to that effect to immigrate, or that, at least according to Israeli law, is how it's supposed to be done.
The issue of "who is a Jew" is a hotly debated one in Israel. The intention was NEVER to let in non-Jews.