Sorry but that's not accurate at all. You are referring to the cash based method of accounting. The vast majority of companies use accrual based accounting.
Quick difference: Accrual based accounting states that you can recognize it when it is "earned". Depending on the product the definition of "earned" differs. If you still have a "significant obligation" outstanding then you cannot recognize the revenue. However, if you ship a product, let's say a ceiling fan to Home Dept, you can recognize the revenue at the time of the shipment despite the fact that HD has not paid you the cash yet. HD might have 30 or 60 day terms to pay you so you don't collect the cash until then but you have recognized the revenue when you ship it. Same goes for cost. You recognize the cost when you "incur" the cost not when you pay out the cash. Here's a simple article outlining the differences: http://en.wikipedia.org/wiki/Comparison_of_cash_and_accrual_methods_of_accounting
You can find out a ton on how companies are doing with all of this based on their Statement of Cash Flows.
That is correct, accrual accounting is mandatory for the corporate structure and recognition of income is recorded at the moment it is earned, not necessarily when payment is made. This more accurately meets the matching principle of GAAP, which stipulates that earnings and associated expenses should be reported in the same reporting period to more accurately reflect the business ability to produce profit. I think what is not clear here and what they may be referring to as not meeting this principle would have to lie in whether or not they reported the associated expenses with those earnings. If not, they are definitely not complying with the GAAP reporting requirements and are overstating earnings for the period.