I think compiler writers understand this "C is a portable assembler" entirely differently than regular compiler users, because compiler writes are in the trenches all day long and focus (too much?) on relatively minor code generation and memory model details which are just not relevant for most compiler users in their day to day work.
Of all the popular high level languages, C is still (among) the closest to CPU and memory, especially when taking compiler specific language extensions into account which are often simply not available in even higher level languages.
And while modern compilers do all sorts of funky and sometimes surprising code transformations in their optimizer passes, I can still look at a piece of C code and the compiler's output as assembly, and figure out which parts of the C code result in what parts of the assembly code. Some parts may be massively reduced, some parts expanded (e.g. by loop unrolling), some parts may have disappeared completely or shuffled around, but the relationship is still recognizable.
Also, from the POV of a programmer in the 70's or 80's who's used to manually stamping out separate programs for each CPU type in assembly, and then switches to C and only needs to write code once which then runs on different CPUs as if by magic, C would absolutely count as a "portable assembler", and I guess that's the origin of that phrase.
