Israel cannot have her cake and eat it. It cannot claim legitimacy by using the United Nations resolution to establish Israel and then reject UN enforcement to keep Israel responsible to international law on the one hand. If UN rulings are now illegitimate, they were also invalid at the time of Israel's establishment.
On the other hand, Israel can have it both ways. She can reject any responsibility for the Palestinian refugees or their descendants, but still expect them to acknowledge her own status as a refugee population. This is possible because under Israeli law, being a refugee is not actually a crime or negative attribute, so long as you don't attempt to take advantage of government assistance programs.
In conclusion, yes, Israel can have it both ways. There are many actions that Israel can take that would not damage its case for legitimacy but would seriously harmate its reputation as a country that respects human rights.
The prevalent depiction of Israel's origin is that it was founded by the UN, that the world backed it, and that the US federal establishment supported it. All of these assumptions are plainly false. Israel was founded by Zionist Jews who fled Europe for Israel because of Hitler. The support came from Western countries who wanted an American-Zionist ally in the Middle East.
Israel's founding document, the Declaration of Independence, states that its existence is based on "withdrawal from foreign occupation" and "restoration of our national home". This means that Israel exists because there were people who needed it to exist, rather than the other way around. The document also mentions "the right of return" for refugees, which assumes that some Palestinians would like to return to what is now Israel.
In reality, there were no Palestinians left in Israel when it was founded. They had all been expelled or died. Now, many years later, some Palestinian refugees do want to go back, but this is not because of any connection with Israel's founding - it's because their homes were destroyed by Israel's wars with its neighbours.
There have been attempts over the years to include in Israel's curriculum materials that dispute its history, such as those claiming that Abraham was not a Jew and that the Holocaust never happened. However, none of these materials has become mainstream.
Israel is a member of the United Nations as well as a variety of other international organizations. After negotiating peace accords with Egypt and Jordan in 1979 and 1994, respectively, Israel maintains full diplomatic relations with each of its Arab neighbors. However, it does not maintain formal ties with Syria or Lebanon because they are not recognized by Israel.
In addition to these nations, Israel has signed agreements with India, the European Union (EU), Japan, Russia, and several other countries. Israel has also established cooperative relationships with many countries through trade agreements and other means. For example, Israel purchases a significant amount of its oil from Europe.
These relationships often include clauses that require either party to be willing to negotiate with Israel if Palestine comes into being. Many countries will not deal with Palestine until it signs a peace agreement with Israel. As long as Israel refuses to do so, they will not recognize the Palestinian government.
Because of this, most people think of Israel as a country that is isolated on earth. It is alone among the nations of the world because it was born out of violence and defines itself as a Jewish state. Although Israel has many friends, it cannot enter into official negotiations with any other country because it is not ready for such contact.
Israel is regarded as the "Occupying Power" by the International Court of Justice, the United Nations General Assembly, and the United Nations Security Council. The court found that "Israel's establishment of settlements in the Palestinian territory occupied since 1967 violates international law." The general assembly declared that these settlements are illegal and constitute a violation of international law. The security council has passed several resolutions against Israel for its construction of settlements.
Israel disputes this characterization, arguing that it only acts to protect itself by establishing civilian communities inside Palestinian territories while obtaining authorization from the government of each successive administration. Some countries may have reservations about criticizing Israel before they vote on their positions at the security council, but no country can veto a resolution approved by the general assembly. Therefore, every year when states vote on whether or not to extend the mandate of the peacekeeping operation, they are implicitly voting on whether or not to recognize Israel's right to exist.
The legal status of Israel within the framework of international law has been summarized by several judicial bodies. The ICJ issued two advisory opinions on the question of Israeli settlements: one in 2004 and another in 2009. In both cases, it was concluded that the settlements were illegal under international law. However she died before the case could be resolved.