There is a facet of truth to your statement, unfortunately it is far from a complete picture for the huge increase in population of palestinian arabs. There are several reasons why they did no remain static at about half to 3/4 million persons.

#1 the exclusion of non-jewish labour from Palestine was becoming prevalent. The Jewish fund held that all land acquired from Arabs be held as inalienable Jewish property, not to be sold or leased to others. This meant Pelestinian feudal holdings, bought from under them from the ottoman owners, often found themselves put off from long worked land. There are notable exceptions though:
Dr Ruppin, from his memoirs records that he had to turn to Arab Labour to build Tel Aviv as it couldn't be done with Jewish labour only. The two factors for this being Arab knowledge of building on that ground, and their cheap labour. Indeed the first house built by the Jewish labourers collapsed under construction.






#2 Infant mortality: It dropped dramatically before fall of the Ottoman empire. The leading Israeli demographer Yehoshua Porath documents this explosion thoroughly in his works.


As all the research by historians and geographers of modern Palestine shows, the Arab population began to grow again in the middle of the nineteenth century. That growth resulted from a new factor: the demographic revolution. Until the 1850s there was no "natural" increase of the population, but this began to change when modern medical treatment was introduced and modern hospitals were established, both by the the Ottoman authorities and by the foreign Christian missionaries. The number of births remained steady but infant mortality decreased. This was the main reason for Arab population growth, not incursions into the country by the wandering tribes who by then had become afraid of the much more efficient Ottoman troops. Toward the end of Ottoman rule the various contemporary sources no longer lament the outbreak of widespread epidemics. This contrasts with the Arabic chronicles of previous periods in which we find horrible descriptions of recurrent epidemics—typhoid, cholera, bubonic plague—decimating the population. Under the British Mandate, with still better sanitary conditions, more hospitals, and further improvements in medical treatment, the Arab population continued to grow.

The Jews were amazed. In spite of the Jewish immigration, the natural increase of the Arabs—at least twice the rate of the Jews'—slowed down the transformation of the Jews into a majority in Palestine. To account for the delay the theory, or myth, of large-scale immigration of Arabs from the neighboring countries was proposed by Zionist writers. Mrs. Peters accepts that theory completely; she has apparently searched through documents for any statement to the effect that Arabs entered Palestine. But even if we put together all the cases she cites, one cannot escape the conclusion that most of the growth of the Palestinian Arab community resulted from a process of natural increase.

Jehoshua Porath, Proffessor Emeritus Hebrew University. reply to Joan Peters.
http://www.nybooks.com/articles/5249


The article actually deals pretty thoroughly with most demographic issues, and there are few who would try to take issue with Porath's credentials.