The term "consulting fee" is not necessarily a euphemism in this context. There are times when firms legitimately need to pay consultants as they do business in an unfamiliar country. However, the term is often used to disguise the fact that firms are paying bribes, generally to government officials in the country where they are trying to do business.
Bribery is very common in international business, particularly in less developed countries. It is easy to disguise the bribery by calling it a consulting fee because it is difficult to prove that someone did not do consulting work for a firm.