Engineering, in a broad sense, can be defined as the application of science to solve problems.
We have all sorts of engineering, mechanical, electrical, software, civil, etc. Each of these disciplines can be used to solve problems and to keep people safe, to save lives and to perform mission critical applications. It would be hard to imagine accepting "alternative engineering". If a company answered a request for quote from a state government by saying that they were using an alternative form of engineering, developed by ancient Chinese engineers, it really couldn't get through the process. If the company made the claim that all of the engineering firms that normally pitch and win contracts are actually conspiring to keep bridge prices high, and to keep bridges constantly in danger of failing just to perpetuate the need for engineering bridge-building companies, the state government would most likely think of the company as cranks and would throw away their business cards. But if they believed the company's claims, even a little, they might ask that company for evidence of those claims, and they'd certainly require a pilot study and proof of these better, cheaper bridges before they (the government) would allow their voting constituents to drive their cars on these new bridges.
The same is true for any kind of engineering that is important, like air traffic control software, medical equipment for hospitals, airframe manufacturing, etc, etc, etc. We demand these engineers, organizations, and companies use the best practices which have been proven by science. Stepping away from the long-standing traditional, tried-and-true path of building these things happens, but only after the process is thoroughly vetted against the traditional methods with plenty of science and testing behind it. Again, this is for mission critical or life-supporting applications.
Medicine is a kind of engineering in this sense. It is the application of basic science to solve a life-saving or life-supporting function. It is certainly more directly critical to those clients who seeks its services. Why are we so much more willing to accept "alternative medicine" than we are to accept "alternative engineering"?