There's some overlap. Altera FPGAs have lots of fixed-function blocks on them, ranging from simple block RAMs to fast floating point units. There's a good chance that Intel could reuse some of their existing designs (which, after all, are already optimised for their manufacturing process) from things like AVX units and caches on x86 chips. A lot of the FPGAs also include things like PCIe, USB, Ethernet and so on controllers. Again, Intel makes these in their chipset division and, again, they're optimised for Intel's process so being able to stick them on FPGAs instead of the Altera ones would make sense.
The main reason that you're probably right is that Intel is generally pretty bad at getting their own internal divisions to play nicely together, let alone ones that are used to being in a completely separate company.