OK, so the method of inactivation of live influenza virus, once it has been isolated from eggs or cell cultures, is conducted by a technique which has been "validated", as it is called. These validation tests have been conducted for decades, and are proven (by subsequent, very sensitive attempts to use the virus to infect cells) to destroy the ability of the virus to infect. The likelihood of these well-established techniques to allow viable virus to survive is effectively zero.
In the live attenuated vaccine (which is given almost exclusively children aged between 2 and 18), the virus backbone is based on a natural variant that only replicates in cold temperatures around 25C, which are found in the nose (hence the reason for giving it as a nasal spray). It is biologically incapable of infecting cells and replicating at 37C, the temperature in the lungs which is the only place in the body where flu infection can occur. So while it can generate an immune response and fight off actual infections, it can't itself cause flu.
In the recombinant form of the vaccine (which is given mainly to over 65s and younger susceptible people), some of the important components of the virus (usually the H part - standing for haemagglutinin - of the so-called H3N2 "super-flu" strain, for example) are produced in insect cells, then purified and administered to induce an immune response to the whole virus. There is absolutely nothing about these purified proteins that can cause a flu infection in any scenario.
Hope that is clear - sorry if it is still quite complicated.
