Your friend doesn't know enough about the subject to be talking.
The transistors and other semiconductor devices on the chip carry out most of the work.
Passive components (resistors, capacitors, inductors) have a part to play in the proper function of most ICs, but without the semiconductor devices (transistors, diodes, etc.) on the chip the passive parts wouldn't do much.
There are highly paid engineers who spend their days designing transistors of various types and sizes and properties. They aren't doing it just for fun. Those transistors are important.
The chips in the ICs are so small and operate so fast that things you wouldn't normally consider can become problems.
At the frequencies some chips operate at internally, the metal conductors act like inductors. I mean, wire always acts like an inductor to some extent but you can ignore it because the inductance is so low. Not so in an IC where the rising edge of a signal may only be picosends wide, and nanohenries of inductance can smear the edge into uselessness.
The same goes for capacitance and resistance. There is always a bit of capacitance between two wires or resistance in a wire that you generally ignore. In an IC, those small effects can become very important.
Those effects are not the main function of the IC, though. Those effects are things that will prevent an IC from working if you don't account for them.