I have a prototype of this product, all connected with wires (buttons, pots and everything).
Only the MUXes are on a small custom PCB with the microcontroller, never had a problem like this... but I understand what you mean.
So basically if I will design the big PCB again should I go for external pullup resistors even for the onboard push buttons ? should I be worried that the current onboard buttons can float as well ?