In 10 years "they" will still be saying learn C because C is nothing but a glorified assembly language with some syntactic sugar. C shows you how your computer works.
It's possible to be a solid C programmer (ie clear understanding of pointers, stack vs. heap, etc) while still not having the depth of knowledge one gets from understanding at least some assembly. When I first learned about the concept of stack overflows (ie as explained in Smashing The Stack For Fun And Profit: http://insecure.org/stf/smashstack.html) my understanding of C really expanded, mostly through the added insight provided by thinking about C in the context of assembly.
It's possible to be a solid C programmer (ie clear understanding of pointers, stack vs. heap, etc) while still not having the depth of knowledge one gets from understanding at least some assembly. When I first learned about the concept of stack overflows (ie as explained in Smashing The Stack For Fun And Profit: http://insecure.org/stf/smashstack.html) my understanding of C really expanded, mostly through the added insight provided by thinking about C in the context of assembly.