It is a well known fact that children from foreign families have a big disadvantage in school. End of story.
It is not a well know at all. All the research done in this regards is pretty much as valuable as arguning whose god is better and more powerful. In a word: useless.
My daughter is perfectly bilingual. Along with other perfectly bilingual kids from her class (mostly Spanish/English) she received over a dozen of full scholarship proposals from the best universities. These were not sports scholarship offers either. On the other hand, most native Canadian kids ended up in lower grade schools at best. More than a few landed on McDonald's kind of jobs, a few are leaching the welfare system.
What you write is an urban legend that is based on some flawed research which considers only linguistic backgrounds without giving much attention to social aspects. Immigrant children are often the children of, for a lack of a better expression, blue collar class. Frequently, they lack academic aspirations because they do not have examples to follow. But even that is not a rule, as many families do see the benefits they, and their kids may have not had in their original countries.
Language is not just a bunch of words and rules of grammar. Another language helps people achieve this additional angle of view on pretty much all aspects of life. The multitude of meanings of words, and the multitide of ways to understand words, concepts and reality, which speaking more than one language affords, allows them to have more flexible and original minds. That, however, is only a potential, not a guarantee.
After all there are also examples of people who learn and achieve a degree of proficiency in languages other than their native ones, and yet they are utter fools who cannot see beyond the ends of their noses, or outside their 5 bedroom houses. These people are commonly known as home grown philosophers.