Of course, if you take two different pieces of software and implement one in assembly language, and the other in high level, you can't claim valid comparison.
But if you take one algorithm and implement it in both languages, assembly implementation will always be faster, thus the basis for their claim.
That's equivalent to claiming Assembly is always faster than other languages, because every program is just an algorithm. It's completely incorrect - I guarantee you I can write an implementation of an algorithm in Assembly that is slower than the same algorithm implemented in Ruby.
I think the person is trying to point out it is you need to be a good programmer to write good assembly, and the a assumption that you will always have a good programmer can be broken sometimes. An algorithm may be an algorithm, but sometimes an inexperienced programmer could easily make it slower.
But if you take one algorithm and implement it in both languages, assembly implementation will always be faster, thus the basis for their claim.