The OP is talking academic secrets and essentially office politics. I've had some experience with such secrets and getting around the politics so will chip in!

(1) Some Academic Ground Rules

Some high end research universities state that the requirement for a Ph.D. dissertation is "an original contribution to knowledge worthy of publication", and the usual criteria for publication are "new, correct, and significant".

(2) Career Secret

In technical careers, say, based on math and computing, there is almost always more money to be make in making valuable applications of such knowledge than in research creating such knowledge. Moreover, for the goals of financial security or even to be financially responsible and to be able to buy a house, have two late model cars, support a wife and family, have a valuable IRA, etc., it can be tough to meet these goals as a prof doing research and much easier making valuable applications.

(3) A Career Success

I was a ugrad math major but by luck stumbled on to a cute fact: There was and likely still is good money to be made applying math, physics, and computing to problems in US national security around DC. So, at the time, some of the math was numerical integration, root finding, numerical linear algebra, the fast Fourier transform, power spectral estimation, digital filtering, lots of applied statistics, numerical solutions of the Navier-Stokes equations, max-min and game theory for the SSBN fleet, etc. My annual salary was six times the cost of a new, high end Camaro.

The success was an example of (2) of more money from applications than academic research.

So a lesson: With math and computing, to make more money, concentrate on valuable applications and not academic research. Further, do this where there are powerful customers with deep pockets for solutions to technical problems -- e.g., US national security around DC.

(4) An Academic Success

I was getting paid so well for what I knew in math and computing that I wanted to learn more so went for a Ph.D. Then right away, as in the OP, politics hit me.

Then I stumbled onto a solution: I saw a math problem (a tricky issue in the Karush-Kuhn-Tucker conditions), asked for a "reading course", maybe not to get a solution but just study the problem. Two weeks later I found a solution that was clearly publishable (later did publish in JOTA).

Presto, bingo, secret discovered: The original work gave me a shiny halo and a Kevlar suit of armor against any and all obstacles, especially political.

Technically from (1), the work was enough for a Ph.D. dissertation.

Lesson: As a Ph.D. student, ASAP do some research that meets the criteria in (1).

(5) Another Academic Secret

Get a Ph.D. in an engineering school and not in a school of arts and sciences. I.e., get a Ph.D. in applied math for some engineering and not pure math without clear applications.

So, for a dissertation, start with an important practical problem got likely from outside academics. Then use some old pure and new applied math to get a valuable solution. Then, since the practical problem has likely not already been solved well, the work will be "new". Since the problem is important and the solution valuable, get "significant". Since the core of the work is some math with theorems and proofs, it is relatively easy to be check the work and, then, be "correct". Since the problem is from outside academics, your profs might not know about its practical details and, thus, can't easily criticize. Also generally the university might like the idea that you are trying to make money because otherwise they can't even hope that you will donate a lot of money!

(6) Business Secret

Currently there is an historic business opportunity: E.g., for less than $2000 in parts, as a Web server I plugged together a mid-tower case computer with an AMD FX-8350 processor with 64 bit addressing, eight cores, and a standard 4.0 GHz clock, an Asus motherboard, 16 GB of error correcting coding (ECC) main memory (both the processor and the motherboard support ECC), several TB of rotating disk, Windows 7 Professional, etc. So, computer hardware and software for operating systems, middle-ware, utilities, etc. are cheap and powerful. In addition the Internet spans nearly all the world, and data rates of 1 Gbps are readily available in the US.

Since these cheap, powerful resources have not yet been fully exploited, there should be opportunities to make significant bucks.

Next, one of the standard remarks is, for success, good problem selection is important:

Well, then, broadly can provide new, valuable information. Using some pure and new applied math can help get more valuable information.

Then with all of that, also pick a problem can solve as a sole, solo founder funded from own checkbook. An example is the Canadian romantic matching Web site Plenty of Fish -- one guy, two old Dell servers, Windows with .NET, ASP.NET, and ADO.NET, ads just from Google, and $10 million a year in revenue. Later he added staff and sold out for IIRC $575 million.

Points: Here we have an example of (2), valuable practical applications instead of academic research. As a self-funded sole, solo founder, get to avoid office politics, co-founder disputes, and venture capital firms and get to own 100% of the company.