The point is that they are not technically pyramid schemes - there is a product to sell. It just so happens that the product is worthless so it makes the system a pyramid scheme in practice, but its peddlers are very quick to point out that it's not a pyramid scheme because of this technicality. It's the same reason why they are still unfortunately legal.
AFAIK there are laws against pyramid schemes, but MLMs are okay. Also, MLMs are pyramid schemes with extra steps, so they are basically the designer drugs of financial hucksterism.
No, the previous commenter is incorrect. Pyramid scheme is a well defined category of fraud. A MLM/affiliate marketing company may be a pyramid scheme, or it may not. Courts have routinely ruled that the business category is perfectly legal.
No. This term was created by pyramid scheme firms themselves to to categorize their business in a legit sounding way.
The person you're replying to really means to say "euphemism," or inventing a new term to avoid the negative connotations of an existing term that already fits. Sometimes euphemisms are motivated by political correctness, but not always and definitely not in calling a business model mostly indistinguishable from illegal pyramid schemes multi-level marketing.
Running a "pyramid scheme" is a crime in many places, so news organizations and such will prefer to use more neutral language that doesn't necessarily imply the groups they're talking about are criminal.
People are more likely to avoid doing business with you if you call yourself a pyramid scheme. Calling youself a "multi-level marketing" business sounds far more benign.