Why did Kolmogorov publish Karatsuba's algorithm?
This paper, in Russian, 


  Gricenko, S. A., Karatsuba, E. A., Korolyov, M. A., Rezvyakova, I. S.,
  Tolev, D. I., &amp; Changa, M. E. (2012). Scientific contributions of A. A.
  Karatsuba / Научные достижения Анатолия Алексеевича Карацубы.
  Современные проблемы математики, 16(0), 7-30.


states the following (items 1—3).


Karatsuba presented his algorithm at a seminar led by Kolmogorov. 
Kolmogorov prepared an article that had two results of his students, Karatsuba and Ofman. One of the results was Karatsuba's algorithm, the other was an unrelated result of Ofman.
The article clearly attributed the results. It stated that the multiplication algorithm is due to Karatsuba and the other result is due to Ofman.  


We can only guess why Kolmogorov did that. I am afraid that the only person who could answer the question why Kolmogorov published the paper without Karatsuba's permission or knowledge was Kolmogorov himself.  Perhaps he thought that it was a good way to publish the results of his students. Note that the article correctly attributed all results. The article of Karatsuba and Ofman was published in the Proceedings of the USSR Academy of Sciences; it is my understanding that it had to be submitted/presented by a member of the USSR Academy of Sciences.

Here is the relevant quote from the paper of Gricenko et al (in Russian):


  Этот результат был доложен Анатолием Карацубой на семинаре А. Н.
  Колмогорова в МГУ в 1960 г., после чего семинар был Колмогоровым
  закрыт. Первая статья с описанием этого метода [2] была подготовлена
  самим Колмогоровым. Там он представил два разных и не связанных друг с
  другом результата двух своих учеников, и хотя в статье Колмогоров
  четко отметил, что одна теорема (не связанная с быстрым умножени- ем)
  принадлежит Ю. Офману, а другая теорема (с первым в истории быстрым
  умножением) принадлежит А. Карацубе, эта публикация под именами двух
  авторов надолго сбила с толку читателей, которые полагали, что оба
  автора внесли вклад в создание быстрого умножения, и даже называли
  этот метод двумя именами.


English translation:


  This result was presented by Anatoly Karatsuba in A. N. Kolmogorov's seminar at the Moscow State University in 1960, after which the seminar was closed by Kolmogorov. The first article with the description of this algorithm [2] was prepared by Kolmogorov himself.  In it he presented two different results from his two students that were unrelated to each other, and although Kolmogorov clearly noted in the article that one theorem (unrelated to fast multiplication) belonged to Y. Ofman, and the other theorem (with the first fast multiplication algorithm in history) belonged to A. Karatsuba, this publication on behalf of the two authors for a long time confused readers, who supposed that both authors had stake in the invention of fast multiplication, and even referred to the algorithm using both names.