I may be uniquely qualified to answer this question. Most of my work centers around development, but I also hold a design degree and have plenty of experience on the creative / UX side as well. I agree, it's rare. ;)
I generally agree with the 'jack of all trades, master of none' sentiment; however with the caveat that it's all a matter of degree rather than a boolean master vs non-master. I have been running an interactive firm for the past 15 years and have done branding, marketing, design, UX, frontend development, backend development, server admin, database admin, and everything in between. I would consider myself a 'master' in only a handful of those areas. In general, people pursue mastery of things that they enjoy most and only become competent in other things out of necessity. While I do have a design degree and have a great foundational education in it, I generally prefer development. But I still use that design foundation frequently when necessary, as in situations where there is not a separate person to handle the design.
Instead of level of skill or 'way of thinking' being the mitigating factor, I would contend that in many cases (such as my own) it is more a matter of available time and interest. Good design takes time, and so does good development. Hiring one person that is good at both will save some time and money, but it will not halve your costs or time. You can expect the right person to be more productive in that there will be a cohesion about the design and development process, less miscommunication, and less poor assumptions.
A hybrid designer / developer will design things that they know how to code (or at least have a general idea). That is a bad thing if his/her development skills are poor, because he/she will be afraid of designing something he/she has no idea how to code. But if his/her development skills are good, it will open up all kinds of possibilities for the design that a specialized designer may not think of or may not think are possible to develop. And even if the specialized designer does come up with a great design that is possible to code, the more interactive it is, the more time and energy will need to be spent conveying the actual interaction rather than simply the static visuals to the separate developer.
But make no mistake: a person's skill set usually aligns with their interests. For example, for me personally, my interest in typography does not keep me awake at night. Even though I have had formal training and always strive to use type appropriately, you will not find me designing my own typefaces or spending a lot of time on kerning a headline. But I will tweak a general layout and design of an interface for quite a while, and how to solve an interesting frontend development problem will keep me up at night. Here is how I would rate my proficiency in the theory, tools, and execution of some relevant skills (and I am doing this only by way of example, not to brag!!):
Frontend Dev: 90%
Backend Dev: 70%
Server Admin: 40%
DB Admin: 40%
% based on perceived proficiency in comparison to those considered 'masters.' I may be doing myself a disservice with some of those numbers, but I'm trying to humble and it's only an example anyway.
If you have the money to hire a separate designer and developer who are both very proficient at their specialties, by all means you should do so. And if you have even more money and can hire a separate frontend developer and backend developer, do so. And if you have even more money and can hire a separate designer and UX specialist, do so. As the company grows you will split roles to be more specialized, that's just the way it works.
But even specialists need to have a working knowledge of related disciplines, or you'll be asking for trouble. Interactive design is different from print, so don't expect a wonderful poster designer to be a good web designer. (This is actually a pretty big issue with this in the company I'm working for right now, where an outside designer who clearly has little web design experience is creating extra work for me because she's not taking into account our target audience's screen sizes.) The concerns of frontend vs backend development overlap but are not identical, etc.
In summary, proficient hybrids exist, but I agree that they are rare. If you are just starting out, I recommend finding one. And when you do, just understand that proficiency is a matter of degree rather than just master or non-master. Ask candidates to rate themselves in all the areas that you want them to be responsible for, then ask them to back up their claims with work examples and/or explanations. IMO a candidate that is 70%+ in all required areas is much more valuable that someone that is 100% in one area and poor in others when the business is small. Or, you could hire someone with demonstrated proficiency in almost all the areas you require and then contract out to make up for the deficient area. As the business grows, split roles and specialize, allowing people to follow their passions.