Not true

Having worked in many 3rd world countries, "illegal immigrants" pick and choose very carefully as to:

1 - Ease of entry and probability of not being deported. Can I get the rest of my family in behind me?
2 - Economic advantage. What level of welfare is readily available?

On the other hand, Refugees, by definition, are running from something to the next safe haven. They're not as choosy. 

The folks crossing from the US to Canada are not Refugees