I am not a tax guy, so if this is capital gains, is it like capitol gains on real-estate. If you sell your home for more than you purchased it for, but then purchased a more expensive home after the sale of the 1st home. No capitol gains is due. So if you purchase a new vehicle that costs more than what VW gave you on the sell back, is no tax due? From what I understand from talking with the VW lawyers last year, VW is not reporting what they are giving us for our VW's to the IRS. I am sure they are writing off something though.
Houses are not the same as cars under the tax code. What you said is mostly correct regarding houses for personal use.
For cars, your basis is what matters. Some examples:
If you bought a TDI for $20k in 2011 and VW is giving you $25k, you owe long term capital gains (owned for >1 year) on that $5k, assuming you didn't make any improvements to the car (maintenance is not an improvement). Long term capital gains varies from 0% to 20%, depending on your tax bracket.
If you bought a TDI for $20k in 2017 and VW is giving you $25k, you owe short term capital gains (owned for <1 year) on that $5k. Short term capital gains = income, so you are taxed at the same rate as the rest of your income (10% to 39.6%).
If you bought a TDI for $20k in any year and VW is giving you $19k, you owe nothing.
And yes, you can simply not report, as VW is not reporting these payments to the IRS. If you are audited and caught, you will pay back taxes and massive fines. If you sell 1 or 2 personal vehicles, you're probably fine. As someone doing this as a business, I have reported all profits.