Other clients tell me that they heard that if a dog is allowed on the couch, this could lead to aggression.

So, let's look at the original question. Should dogs be allowed on the couch?

The answer is, if you want your dog on the couch, let him lie on the couch. If you don't, that is fine too.
A lot of people have very nice couches that don't mesh well with a hairy pup, no matter how cute he or she is. That is totally understandable and your choice. 

I will look at the two most common concerns about having a dog on the couch and try and dispel any concerns you might have.
Dog Training 

Myth # 1
Dogs will become the "alpha" if they are allowed on furniture. This philosophy has become popular by trainers such as The Dog Whisperer and others that talk about making sure you are the "leader". This includes ridiculous, unfounded suggestions such as making sure that you go through doors before your dog, that you eat first, and that your dog is not allowed to walk even 2-feet in front of you on a walk.
These ridiculous suggestions gain momentum from untrained or improperly trained dogs ruining it for the rest of the dog community, leading to countless dogs being manhandled and mistreated in the guise of dog training. The advocates of these methods often make it seem like dogs should do as we please when we please.
If they don't heed our every whim then the trainer needs to step up the physical methods until the dog knows who the "boss" is. 

Any memory planted from first-hand experience with a dog that is allowed to run rampant through the house, terrorizing guests, destroying furniture and barking at everything can strike fear in the new dog guardian.
"If I don't take charge RIGHT NOW, my dog will be like the Taylor's dog that I knew growing up. I definitely DON'T want that to happen."
The new dog guardian then feels that they need to be tough, show discipline, and "be the boss" to avoid problems in the future. What frequently happens is that dogs are unfairly punished for just acting like normal dogs. There have been so many occasions that I have been hired by someone that has a dog that is destroying the furniture, but they don't think it is fair that they use a crate or baby gate in another dog-proofed room.
They just want their dog to stop chewing on the furniture. The answer is simple; don't allow the dog to be near the furniture unless you are watching. If you can't watch your dog, put him in the crate. Period. 

Many dog "problems" can be stopped before they get started if there is forethought and understanding. A dog will never learn that the antique dresser tastes "yummy" if he is not allowed to chew on it.
If a dog is managed and trained properly, it is amazing how they become better behaved. Does that make you "the boss?" I would say it makes you someone that is intelligently setting ground rules and making sure you prevent your dog from learning bad habits.

If dogs are trained properly, given enough mental and physical exercise, socialized properly, and kept from exhibiting escalating behaviors that cause aggression, then they will happily coexist with your family.
If you adopt an older dog that is lacking in any of the areas mentioned, you can still humanely train him or her without resorting to archaic and abusive training methods including "alpha rolls" and more physical methods "to put a dog in its place".
Dog Training Myth #2
Dogs on the couch can lead to aggression. I also frequently hear the same concern about dogs on the bed. I have also heard that dogs "need to be at a lower level" than people so they know their place "in the pack".
There is not basis to these claims taken at face value. 

In other words, if you have a well socialized dog without handling issues, territorial aggression or resource guarding and allow him on the couch, this will not turn him into an aggressive dog.
The history of this myth probably stems from dogs that DO have handling issues, territorial aggression or resource guarding issues. Dogs that have one or more of the above issues might bite someone if they are on the couch or bed. But, the act of lying on the couch or bed did not CAUSE the aggression.
This is when the aggression shows up and is noticeable. 

If your dog has any of the above issues, find a qualified positive reinforcement trainer in your area. Don't hire anyone that uses choke chains or prong collars, or shock collars. Using these methods are unnecessary and can make the problem worse.