You're grouping carries. If you have 13 spare bits, you can accumulate 13 additions before you have to take care of carries. Then you have to add some overhead for bit manipulation, but the article's point is that the parallelism gains more than make up for the bit manipulation.
You are reducing the number of carries. The article explains it clearly. If you're not convinced by the article, I won't try to convince you. (Edit: the last thing I'll add: you are reducing the number of carries for 64-bit additions. When adding 13 51-bit numbers, that does not count as carries instruction-wise, as it's still add, not adc.)
I see what I was doing wrong, I was considering total bit carries during the addition, ie... 1+1= 10 and is a one bit carry, and not the carry operation done after overflowing the word boundary.
Next time, I'll keep from reading tech articles while running on too little sleep.
