My understanding of history is that all the native non-jewish "Palestinians" were offered full citizenship in the new Israeli state, and that some or at least one became MPs.
Not true.
If that had been done, it wouldn't be a Jewish state, because something like 70 percent of the population wasn't Jewish at the time of independence. The idea was to carefully draw the borders so that a Jewish majority would be guaranteed; even then, they still ended up with 20 percent non Jewish.