I think PICs are certainly RISC. ... Arithmetic is only between registers I believe -- they just have rather a lot of registers (32 or 128) and sometimes no RAM.
I think you've been mis-led by the somewhat weird (archaic) naming conventions used on the 8bit PICs.
A PIC has one general purpose register, an accumulator "W" ("Working Register")And it has a RAM space that includes general purpose memory, which they call "General Purpose Registers", as well as what they call "Special Function Registers" that do peripheral-like things.
"Real Math" (Add, subtract, OR, AND, XOR) occurs only between the W and one of the memory locations, and the result can be stored in either location. Instructions are wide enough to address a substantial number of the memory locations (up to 512 at a time on PIC18) with the rest reachable via bank switching. But I'd say that they're definitely more like memory than registers (for instance, there are no instructions that operate using two GPR locations.)
In addition, there are a large number of "simpler, single-operand, operations" that can be done on any memory location. INC, DEC, (constant)Bit tests and clears, etc. Things that are very handy for a microcontroller to be able to do, but not enough (IMO) to make them "registers." And not very RISCy.