This is very curious, and I would think someone is really misunderstanding something quite badly.
There is hyperthreading, where one core basically handles two instruction streams, without any execution units being added. The total performance for two threads will be closer to the theoretical maximum of instructions that this core could achieve. If you have incredibly good code that gets 80% of the theoretical performance it might go up to 90%. Bad code getting only 30% of the theoretical maximum might go to 60%. It is cheap to do and may or may not improve performance.
But beyond that, you will have n independent CPUs. They will usually be able to perform n times the instructions. Both branches, integer, floating point, and vector instructions.
The only problem you will have is that the hardware for accessing RAM will only exist once. You can bet that this hardware is as efficient as possible. On my personal computer, eight cores cannot use all available bandwidth. Another problem is that some caches will be shared. On my system, there is 24MB of L2 cache, with 12 MB each available to a group of 4 cores. So if two cores are used, one from each group of four, they have 12 MB each. If you use all eight cores, they have 3MB each on average. But that will not cause a slowdown like the one you were told about.
AMD is now building a monstrosity with 64 cores. According to your information that would only be able to perform about 40% more instructions than a single core. Somehow I think AMD ignored that information you were given and built their own reality.
A multi-core processor with p cores where the number of operations per core is divided by 0.7p would be impossible to sell.