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Carl, I want to be sure we are reading this the same way. The rules read that the student cannot receive the refundable credit if the student  earned less than half of their support.  In other words (for practical purposes), the student was , in fact—by default—supported by the parent.

In practical terms, there is no requirement the student be supported by the parents. The student can get their support by numerous methods not involving the parents for one penny. Other than the student's own earned income, there's scholarships, grants, 529 distributions, gifts from Aunt Mary, money they found out the ground, etc. All of that is considered third party support. Even money from the parent is considered third party support for the student. Lets look at the requirements for your typical undergrad, and I'll go into more details.

 - Must be enrolled in an accredited institution

 - Must be enrolled as a full time student for any one semester that starts in the tax year.

 - Must be pursuing a course of study that will lead to a degree or other credentialed certification

 - Must be under the age of 24 on Dec 31 of the tax year.

 - Must not have provided more than 50% of their own support.

 - Must be single, or if married *and eligible* must not file a joint return.

Now those are the requirements that in various places in IRS Pub 970 it's there in black and white.  For students that meet all of the above requirements, their parents are eligible to claim them as a dependent on the parent's tax return.  Note there is no requirement for the parent's to provide one single penny of suppot. The requirement just flat out does not exist.

There are only two possible ways a student can provide more than half of their own support.

 - The student is self-employed or as a W-2 job and actually is paid enough money in the tax year to justify their claim to paying more than half of their own support.

 - The student is the *PRIMARY* borrower on a "qualified" student loan, and sufficient funds were distributed to the student during the tax year to justify them providing more than half of there own support.

That's it. There is no other possible way the student can provide more than half of their own support.

But did you also know that it's perfectly possible for a student to earn $300,000 in a tax year, and yet "still" not be able to claim or justify providing more than half of their own support?  To cover this aspect, we first need to define "support". Here's what the IRS considers support.

 - Qualified education expenses (tuition, books, lab fees)

 - Housing expenses (which includes utilities)

 - Transportation expenses

 - Clothing expenses

 - Food expenses

 - Entertainment expenses

That pretty much covers it for what the IRS considers expenses for "support". The IRS also states those expenses have to be "reasonable" too.  There's an IRS publication somewhere that I can't recall or find now that explains how the IRS determines what is reasonable. But let's assume a student actually earned $300,000 of income in a tax year. Here's how they will "NOT" qualify to claim they provided more than half of their own support.

 Student's suport cost in tax year:

- Housing (including utilities) - $15,600 ($1000/mo rent & $300/mo utilities)

- Food - $4800 ($400/mo which is on the high side really)

- Transportation - $6000 (assuming the student has a car, figure $500/mo for gas, which is on the high side)

- Clothing - $500 (I doubt a student would spend that much on clothing in a year)

- Entertainment - $3000 (that's $250/mo which is high)

- Qualified Education Expenses - $20,000 (that's tuition, books & lab fees which I've made "just barely" unrealistically high.)

So the total support expenses for the year comes to $49,900. So the student would need to have earned at least $24,951 to have any claim of providing more than half of their own support. But here's how that gets nixed.

3rd Party Support received by or on behalf of student:

 - Scholarships & grants - $20,000

 - 529 distributions - $16,000

That comes to $36,000 of third party support. So even if the student earned $300,000 during the year, if they claim they provided more than half of their own support, they better be ready to prove to the IRS that their *REASONABLE* support costs exceed $72,000 for that tax year. I can assure you that's not going to happen no matter where you attended college on this planet - much less in this country. 

The IRS also has restrictions on maximum amounts that can be claimed on some of those items too. Here's a few:

 - Housing (including utilities) If the student is living off campus, then what they claim for housing costs can not be more than what it would cost them to live on campus. The only exception is if the school does not provide on-campus housing, or if the student has a letter from the school informing the student that on-campus housing is not available and they have no choice but to pursue off campus housing. Even with the exception, the cost must be reasonable for the area they are living in. So claiming the cost for a $5000/month suite in Trump Towers is not going to cut it.

 - Food - There are very few colleges that don't offer a food plan for their students. If the school offers on campus cafeterias or what is referred to as a "food plan", then what they claim for food costs each semester can not exceed the cost of the food plan. The fact the student may be working their income producing job when the cafeteria is open does not matter. Exceptions are that if the student is living off campus *not* by their own choice, or if the school does not offer a food plan. But even then, costs must be reasonable. (So no steak and lobster for lunch and dinner every day.)  If the student claims it costs them $1000/mo to eat, that's just not gonna fly.

So as you can see, overall the student's earnings really don't matter at all when it comes to the support question. What the parent's pay for that student's support (if they pay anything at all) doesn't come into play here either.