I think that the people who say this are people who have plenty of money! No, money alone can't buy happiness if there are other non-monetary issues to deal with, but let me tell you that being poor sure as heck doesn't earn you happiness either.
I can totally see what Serendipity said:
I've seen a study that indicates money positively correlates to happiness up until the $50K income level. After that there is not much difference.
When some people are very wealthy, they might begin to buy things that require a lot of maintenance and upkeep, like having 2 homes, an in-ground pool, a boat, etc. Then their lives revolve around maintaining all their stuff, and they don't enjoy them as much. I never aspire to have 2 homes (just seems wrong when there are people in this world who don't even have ONE home!); I just want to live comfortably, and not feel guilty about buying "expensive" unnecessary items at the grocery store like Toaster Streudels for my son!