Having money is clearly helpful for your child in terms of educational opportunities. To me, that is quite obvious.
That doesn't mean your child can't do well without money.
As some posters have mentioned- if both parents have to work long hours (or a single-parent family), that is less time available to supervise homework or do informal teaching at home for the child.
Our community college offers wonderful courses in the summer for rising gifted 5th graders. A one-week half-day course is $250; all day (until 3:30 pm) is $500. When my kids get to that age, we will enrol them- spending $3000 or more for them to take accelerated math, chemistry, etc. Plus we can drive them there and pick them up.
I bet there are many gifted kids whose parents can't afford those courses or take off work to drive them to and from the courses.
I'm sure many of you in your communities have similar types of activities.