I have read the same study as OP and completely agree with it.
While "money doesn't do everything" "money can't buy you love" are not false statement, thinking that money doesn't help is complete bullshit.

Not having to worry about staying alive / in good health / satiated / hydrated / under a roof / ... is a gigantic saving in stress, and money is a HUGE factor.
Many people seem to have a manichean point of view, thinking that the reality is to have either a social life / a loving family or money. Like the romantic view of movies or books, showing poor people happy together, sharing everything they have, etc... Well this is bullshit too. Poverty can be very ugly especially in a few countries.

It would be interesting to conduct this study in the other way : "Can you be happy without a single penny in your wallet ?"

While it doesn't seem impossible to me to be happy without money, most people just dream about getting rich. But in reality, all they want is to not lack of anything.