In a word, no. Morkies are not healthier than pure bred dogs. I have no issue with mixed breed dogs. I love all dogs! I do take issue with anyone who intentionally breeds designer dogs for many reasons, so I believe your gut is correct!
It sounds like you really just need to find a good way to educate your fiance, so he understands the bigger picture like you do.
For a long time, I had heard "mutts" are healthier too, so I understand it's probably something he has heard for years. I guess you can play the google game too.
If you google "hybrid vigor myth in dogs," you will find plenty of pages that speak to exactly what you were saying. Mixing two dogs doesn't mean you will end up with a healthier dog at all. In fact, you could end up with the worst of both breeds.
You might find it interesting to note that the man in Australia who originated the Labradoodle now wishes he never done so, because he believes it helped start the designer dog craze, which was never his intention.
I am very pro-rescue now, and for the longest time I did not understand the point of dog shows...and then one day after reading enough it finally clicked. A dog show is a way to get approval for breeding stock. Because I believe my (way off standard) dogs are the cutest in the world, does not mean they should be bred. You can imagine how difficult it would be to look at one's own dogs through an objective eye. So in theory, a reputable breeder shows their dogs, gains approval for their breeding stock, does health testing on their dogs, and breeds with the goal of the "perfect" Yorkshire Terrier in mind. With so many unwanted dogs in the USA, it only seems logical to me that breeding should be done with a distinct purpose and goal in mind, and that should not be money! Your post makes me think you have grown to love the yorkie breed through your research (welcome to the club!
). Sadly, simply seeking out any old yorkie breeder isn't nearly enough to guarantee you will likey end up with a dog who has those characteristics. It's also important to note that just because someone breeds two championed show dogs that all of their offspring will be show quality dogs. Maybe one or two will be, and here is where the pets who have all the qualities of a show dog (to the untrained eye) are found. Maximo (posted above) has two great pups that are a great example of pet yorkies who closely resemble the standard.
Someone who is breeding morkies or other mixed breeds is doing so with no "goal" in mind. There is no morkie standard, and morkies can look like everything from yorkies with maltese coloring to maltese with yorkie coloring and everything in between. You really don't have much of an idea of what you are going to get when you are mixing two breeds together. I would be very surprised to find of any breeder that mixes breeds who is doing health testing as well. You are certainly not going to find a dog in a pet store that came from a breeder that does health testing. And yes, it is a proven fact that 99% of dogs in pet stores came from puppy mills. I also think a great test is to imagine the kind of person who would breed their dogs an then ship the puppies off (frequently at ages way too young to even be separated from the mother) to the first person who had a credit card to pay for them. A reptuable breeder will always take a dog back if you can no longer care for it for any reason, will offer a health guarantee, and should generally be there to answer any questions you have as you share your life with one of their pups. Additionally, a reputable and responsible breeder will want to make sure that their puppies are not bred, whereas there are no restrictions placed on pet store puppies, which are most certainly poorly bred, are likey to have many health issues, so you can see how quicky it can escalate to where we have so many poorly bred animals with health issues. It is a vicious cycle.
If size is going to to be an issue, perhaps you and your fiance could consider adopting an adult dog that is full grown? Even the best of breeders cannot guarantee size (only give their best guess). It is the only way to make certain you'll end up with a dog the size you desire. Likewise, if you or he really likes the idea of a morkie, the shelters and rescues are full of these cuties. Looking at an adult morkie gives you an idea of how they'll end up appearance wise too since they often change quite dramatically from their apperance as a puppy.
That website sends up a lot of red flags for me, and I would run far, far away from anyone who advertises teacups.
Kudos to you for doing your research ahead of time. I did not, and I have a poorly bred (very adorable) 5 year old yorkie with some health issues that are both financially and emotionally taxing. Even if money is no object, I can't tell you how hard it is emotionally to watch a dog you love so much suffer. One I educated myself I chose to adopt. My other pup is a puppy mill rescue (obviously poorly bred), so it is a shame she was used only to make puppies while living in a rabbit hutch in deplorable conditions, when she never should have been bred to begin with, not to mention she is an awesome little dog with a fun personality once she finally gained the confidence to come out of her shell. No doubt her puppies were probably sold in pet stores. A reputable rescue will have done a full vetting on any dog ready for adoption to make sure they are in excellent health, or they will be sure to let you know of any current or likely future health issues that would need to be addressed so the surprises are limited.
Sorry that was so long. Good luck!