Yes. It’s fair. As long as they follow the proper channels. Same with Mexicans and any other immigrants seeking asylum. Follow the rules. It’s when you shun the system and enter illegally that causes problems.

The ‘proper channels’ aren’t realistic.  The people that come here from the poorer nations aren’t usually in the position to afford the fees, taxes, etc. that comes with being a legal immigrant. 
As native-born Americans, we take our liberty and prosperity for granted a good bit of the time.  Heck, you think most of our ancestors went through the ‘proper channels’?
I understand the anger.  We usually are angry at that which we do not understand- their language, their culture, etc.  And there is some abuse of the system as we pay the taxes that they benefit from ie their kids go to school on our buck.  But the same can be said for the poor in general.
Frankly, it’s our burden.  Basically any job you can get (ie paying min. wage and up) pays much more than most jobs they can get.  We’re talking earning around $50 for a very hard day’s work out in the dirt and in the summer heat. 
And if you want to fix this system, you start with those that hire the immigrants… the ones that escape having to pay them proper wages, or taxes, health care, etc. for their work.
Make no mistake… you wouldn’t trade places with any of these immigrants.
Just like with any group of people, you have your good apples and your bad apples.  From my experience, most immigrants aren’t looking for a handout.  They’re also as hard working as any of us, possibly harder simply based on the fact that they started out with much less. 
And they’re aware that the vast majority of Americans dislike them, even hate them, for wanting nothing more than a chance at what we have.  And we say they can have a piece of our pie, as long as they jump through loopholes that we didn’t have to, and as long as they pay fees, taxes, etc. that we didn’t have to pay.
However, we Americans are full of it.  Yeah, we’ll bitch and moan about them being here, but we still eat the vegetables they pick, live in the houses they build, etc.  If you want to make a real difference, stop using these people that you deem unworthy ie put your money where your mouth is.  But these days we’re not known for our integrity seeing that 99% of our products come from communist China… yet we supposedly don’t support communism.

What amuses me the most is that there’s an application fee, and most of the time, the applicant is turned down.  The applicant is then forced to re-apply and give our government even more money.  Over, and over, and over again.  The instance I’m talking about concerns a relative of someone I know.  She has no criminal record, and most of her family already lives here and are legal residents in the U.S., also with no criminal record.  Her family members are lawyers, nurses, folks in the technology sector, college grads, and upstanding members of our society.  Yet, apparently this woman isn’t qualified enough to be Americans.  Go figure.  Uncle Sam’s getting his money though, and he’s lying to me, you, and himself when it comes to immigration.  Might as well pry that tablet off the Statue of Liberty because we’re closed. 

No Vacancy, amigos.  Lo siento.