The answer to the interview question should be something like:
Possibly, where it matters one should use the types defined in stdint.h, or otherwise consult the compiler documentation or inspect the definitions in limits.h.
The interviewer is unlikely to be asking for a yes/no answer and probably would not appreciate such terseness in an interview situation in any case - the questions are intended to get you talking until you have said something useful or interesting about yourself or your abilities and knowledge. What he is perhaps looking for is whether you are aware of the fact that standard type sizes in C are a compiler/architecture dependency and how you might handle the potential variability in portable code.
It is likely and possible that an int between one PIC and another PIC or one Atmel and another will differ let alone between PIC and Atmel. An Atmel AVR32 for example will certainly differ from an an 8bit AVR, and similarly the MIPS based PIC32 differs from "classic" PICs.
Also the size of built in types is strictly a "compiler implementation" issue, so it is possible that two different compilers for the same processor will differ (although it is highly improbable - since no compiler vendor would sensibly go out of their way to be that perverse!).
Languages other than C and C++ (and assembler of course) are less common on small micro-controllers because these are systems level languages with minimal runtime environment requirements, but certainly the sizes of types may vary depending on the language definition.