Cambridge Dictionary: "We use a lot of and lots of in informal styles. Lots of is more informal than a lot of. A lot of and lots of can both be used with plural countable nouns and with singular uncountable nouns for affirmatives, negatives, and questions." http://dictionary.cambridge.org/us/grammar/british-grammar/quantifiers/much-many-a-lot-of-lots-of-quantifiers

"The first important difference is that 'many' can be used only with countable nouns in the plural, and 'much' can only be used with uncountable (mass) nouns in the singular. There is no such distinction for 'a lot of' and 'lots of', which can be used with both, i.e. both 'a lot of/lots of people' and 'a lot of/lots of water' are correct." https://jakubmarian.com/many-much-a-lot-of-and-lots-of-in-english/

An English teacher: "'A lot of people have worries about grammar' is correct." https://www.quora.com/Which-is-gramatically-correct-A-lot-of-people-has-or-A-lot-of-people-have/answer/Abi-Ru-Shirzan

"'A lot of/lots of' is still felt to be informal, especially in BrE, so in formal writing it is better to use 'many' or a 'large number of' in statements." https://www.italki.com/question/122661?hl=en-us

Genitive.

люди is the nominative form, but много requires the genitive of the noun, which in this case is людей.

I see no reason to reject that. To anyone reading this who entered that, if it was still rejected, please report it.