Dave: of course you can read/write memory without API calls or interrupts, you just can’t write to kernel memory from usermode… whether memory mapped devices would probably be set as kernel.
mccoyn is probably thinking of the CPU feature called paging, included on x86 all the way back on the 80386. It doesn’t involve interrupts though, but does have some caching going on (TLB entries). Modern operating systems use it to provide a per-process view of memory space (CR3 register + paging tables), to translate these virtual addresses to physical addresses, and insulate processes against eachother. Complex topic that deserves a lot more text 