I find this a very interesting question, and like most people I believe that I know the absolutely correct answer. But I am going to try to talk about it from both sides, or as much from the other side of my opinion as I can. Kind of like how Seth Mnookin talks about the anti-vaccine field of thought in his book The Panic Virus. Even though he is pro-vaccine he did do a good job trying to understand what would cause a portion of Western society to be vehemently opposed to them.
If you Google "horses fake lameness" you will find numerous message boards with hundreds of stories from people saying they have had first hand experience of their clever horses fooling them. If individual observation were scientific evidence then it would be a solid fact that horses can fake lameness or illness in order to get what they want. Many people say that the people who don't believe it exists have just never seen it so they just don't know any better.
I'd never thought about it myself until about five years ago. I had a fresh off the track Thoroughbred, just four years old and very hot and very sensitive. The first time I had my farrier in to do her feet, she went lame right after he put on her right front shoe. She was my "delicate little flower" and even the smallest pain was extremely upsetting to her and would melt her 16.1 hh's, 1100 pound body into a quivering pile of goo. After the farrier left she could barely walk and tried leaning against the wall of her stall until she finally gave up and laid down. I was horrified and called my farrier back out to ask him what had happened. Upon looking her foot over he announced, "She's very dramatic. She knows she's supposed to work (in our training) this afternoon so she's faking it to get out of it." Then he left.
My instincts told me that didn't sound right so I called my trainer's farrier. He came out and looked at her foot and said she had what's called a "hot nail" - a nail that was put in too high and was causing her pain. He said not to be too harsh on my farrier because it was in what would be considered a perfectly legitimate spot for most horses, she just had small, sensitive feet and for her she would need the nails to be a bit lower than the norm. He took the nail out, put one back in a bit lower and she was back to her old self and extremely relieved. I was glad to hear my farrier had made an honest mistake, but I still fired him because he told me my horse was "faking it" when she wasn't.
I have since said in conversations among horse people that I don't believe horses "fake it" to get out of work. A little over half the time the other horse people laugh at me and tell me I don't have enough experience with horses to know what I'm talking about, or tell me I should educate myself before saying such silly things. So, I did go ahead and educate myself. I picked up a copy of Evidence Based Horsemanship because I thought, what better way to understand a horse's brain and how they think than by reading the scientific studies of a neurologist. Granted this is only one book and I would like to read a lot more research on how horse's brains work, but I still found the information to be valuable and convincing.
I won't go into everything they talk about in the book regarding parts of the brain and brain activity, but I will say that horses to not have the cognitive ability to plan schemes and deceive. What they do have the ability to do is learn from experience. So, if you continually reward a horse for a certain behavior they will learn to continue to do that behavior in order to receive their reward. This is the most basic example of how horses are trained. It is possible if your horse bucks and you get off and put him away, and then he does it again and you get off and put him away again, his brain circuits will equate bucking with a pleasurable response - and if you keep doing the same thing over and over again he will start to buck every time someone gets on him after awhile. But that is not because he consciously thought, "Hey, this is great. I've totally got her wrapped around my finger!" It is because the horse instinctually (like us) seeks release from pressure and will do the thing he is rewarded for over and over again to find that release from pressure. That is a huge neurological difference from the cognitive ability to "fake injury" in order to get off work.
In a round about way we are also seeking a release from pressure when we are suddenly faced with a horse with a mysterious lameness we can't explain. We go for the easiest explanation which is "he must be faking it to get out of work" - suddenly, right then we are released from the pressure of the stress of not knowing what is causing our horse to show signs of injury or pain. So, we are much more similar in our actions with our horses than we realize. Only we have the cognitive ability to step back and look at our actions and problem solve through planning and analysis instead of just going on our base instinct to be released from pressure (especially if that release is by closing our eyes and believing something that isn't true at the expense of another). When people stop being willing to put the effort into planning and analysis to find out what their horse is truly trying to tell them, it is not the horse who is being lazy, it is the horse owner.
I have not run into this in my massage work on horses yet. Thankfully, every horse owner I have worked with has been a wonderful, caring and well educated horse owner and I've been blessed to be able to work with their horses. I imagine that one day I may have a client who says they think their horse might be faking it, and I hope that I will have the ability to explain to them how that isn't actually possible (despite what folks have observed on the outside) and encourage them to look deeper for the real answer.
And on that note I would like to give a little shout-out to the fact that I had the wonderful opportunity to work on a horse today after she was ridden in a Peggy Cummings Clinic. Not only did I get to watch my client's horse move while working, but I also got to be present for some really excellent riding instruction. That's one of the things I love most about this job is that there are so many incredibly knowledgeable and fascinating teachers in so many different facets of the horse world and there are so many opportunities to learn endless cool stuff.