Is it true that Jews around the world are automatically considered Israeli citizens, even if they weren't born in Israel?

No. They are not. Jews from around the world are entitled to ask for immigration status and citizenship, but it is not automatic.

If they can prove they are Jewish either by family paperwork or through a reputable Rabbi vounching for their Judiasm.

1) Jews around the world are usually citizens of the country where they live. They are certainly not considered citizen of Israel. If they come to spent some time in Israel, they are also not considered citizens of Israel either.

However, "the Law of Return (Hebrew: חוק השבות, ḥok ha-shvūt) is Israeli legislation, enacted in 1950, that gives Jews, those of Jewish ancestry, and their spouses the right to migrate to and settle in Israel and gain citizenship."
Source and further information:
http://en.wikipedia.org/wiki/Law_of_Return


2) "Aliyah (Hebrew: עלייה Translit.: Aliya Translated: ascent) refers to Jewish immigration to the Land of Israel (and since its establishment in 1948, the State of Israel)."

"Aliyah is widely regarded as an important Jewish cultural concept and a fundamental concept of Zionism that is enshrined in Israel's Law of Return, which accords any Jew (deemed as such by halakha and/or Israeli secular law) and eligible non-Jews with immediate Jewish relatives, the legal right to assisted immigration and settlement in Israel, as well as automatic Israeli citizenship. Someone who "makes aliyah" is called an oleh (m. singular) or olah (f. singular), the plural for both is olim. Many Religious Jews espouse aliyah as a return to the Promised land, and regard it as the fulfillment of God's biblical promise to the descendants of the Hebrew patriarchs Abraham, Isaac, and Jacob. Aliyah is included as a commandment by some opinions on the enumeration of the 613 commandments."
Source and further information:
http://en.wikipedia.org/wiki/Aliyah

Further information:
http://en.wikipedia.org/wiki/Homeland_for_the_Jewish_people

Um no. people in America, americans, people in Israel, Israelis.

i consider them Jewish if they're Jews makes it alot simpler and less stereotypical. but im not sure about the citizenship allegation, idk.

I've heard that too.

I think it was in the past but not any more.

Actually there are many countries that can hold dual citizenship with America.

It's not just Israel Regina. Your bias is showing through.

http://www.us-immigration.com/information/dual_citizenship.html

I do know that they are the only people who hold dual citizenship....to America and to Israel. No other citizen of another country can do that....what does that tell us?