There is no NEC requirement (kitchen) for this that I've ever been aware of or can find. The reference in the NEC 210.4(B) requires that the two ungrounded wires which are sourced from circuit breakers will simultaneously trip if a fault should trip one.
I just wanted to comment so this is not assumed to be a correct wiring method.
The NEC changes every four ? years, and the adoption of the latest Code can vary by cities and municipalities.
Things also move and change in the Code often, making it difficult to quote a Code requirement without knowing which Code edition applies.
In my opinion, the NEC is very poorly formatted, and it can be very difficult to find anything since the layout is so convoluted.
Luckily the newer NEC code books highlight the changes from the last Code version, which is a very useful feature, but this does not give you a backwards paper trail beyond four years unfortunatly.
The fact that the NEC constantly changes makes it a challenge to keep up, and I often attend seminars just to keep up with the changes.
And often different Code inspectors interpret the Code differently (sometimes), which really makes it difficult.
I have appealed NEC Code rulings to the local Code folks, and been granted variances, since the bottom line of the Code is to not create any unsafe situations.
For industrial electrical work, some processes can become unstable if you trip off a curcuit breaker feeding the process, such as in oil refineries, and so there are sections of the Code that allow deviances, to prevent creating hazardous situations (such as high-resistance grounding to prevent nusiance tripping).
Hyrdrogenating cooking oil with hydrogen is a process that is exothermic, and you don't want to nusiance trip that process either.
Luckily I do industrial/municipal design work only, and so there are not as many Code changes for those applications, compared to resdential work.
I once had the chief electrical Code guy ask me which version of the Code I was using.
I answered "I use my own Code".
He said "What Code would that be?".
I said "My Code is simple, design things so that nothing burns up or blows up......ever......for any reason".
If you burn something down, it does not matter if that design met Code or not, it only matters that the design failed in that application.
There are often unique situations in municipal/industrial work, and the Code cannot address every unique situation, other than to say the electrical system must be safe, and must operate in a safe fashion in all circumstances (expected and unexpected circumstances).
For industrial electrical design, I often exceed the requirements of the Code, since the Code is a minimum standard, and you almost never want to use minimum standards in industrial/municipal.
I run into high temperature situations, and also classified hazardous areas all the time, and this has to be carefully handled.
Classified areas can have explosive gasses or dust.
Much of what I design is medium voltage, which gets into a lot of IEEE/ANSI standards, and not so much the NEC.
There is a lot more to electrical design than what is in the NEC.
In the NEC 2014 version (NFPA 70), the dual circuit requirement for kitchens is Chapter 2 "Wiring and Protection", Section 210 "Branch Circuits", Part III "Required Outlet", 210.52 (B)(3), "Kitchen Receptacle Requirements".
As I mentioned, I dispise the way the NEC is laid out and formated/numbered, but it is what it is.
I think some of the digital versions of the NEC allow searches? and that would be helpful, but I don't use digital versions (yet).