Not sure what you base your perception of the scope of my understanding on, but it doesn't matter. What I see is people looking to improve their standard of life. Yes, there will be some dishonest ones, as there are dishonest American citizens who were lucky enough to have been born here. Your point seems to be that the percentage of dishonesty among the immigrants is higher because of the fact that they entered illegally, breaking the law. It's a legitimate argument. My take is that for the overwhelming percentage, entering the country is the only law they break, much as exceeding the speed limit on my bike is the only law I break. In my opinion the immigration problem consists of a huge bottleneck in obtaining permanent residency and ultimately citizenship. My sister has a good friend who's parents moved here from Colombia when she was 3. Her parents never naturalized because the U.S. does not honor dual citizenship. To become a citizen you have to renounce your home country's citizenship. To each his own. Regardless, the woman has carried a green card her whole life, renewing it every 10 years. It's always taken about 30 days to get the new card in the mail. This last renewal has almost taken 2 years and she's still waiting. The card expired so USCIS stamped her Colombian passport to extend the legality of her being here, even though she's lived here for 55 years. What is wrong with the process? THAT needs addressed, and in my mind is the immigration problem.
