I can only comment with certainty about what I saw.
I agree, children should never be removed from families because of poverty.
The families I was involved with would not have done any better with an extra £1000 a month (fostering tends to offer more like £500, by the way). They may have done better with a state provided home help. I live in an area where the state offered specialist child minders to families who struggled. It prevented some, not all, coming into care.
As a foster carer, I was not a baby sitter. The children I looked after had significant additional needs. They were hard to keep in school, hard to look after, and I loved them very much. I was paid a princely 60p per hour per child, and was given a similar amount to cover their food, household costs, clothes, holidays, pocket money, birthdays, etc.
As for why there might be lies in the report- I don't know.
Perhaps they confused one family with another, perhaps they felt they needed to get the child away but didn't have time to double check information.
And perhaps they were malicious, there are malicious people in every area.