You asked a few related questions:
My question is - is a credit report actually the source of truth for debt to income calculations? Am I mistaken and instead the consumer is trusted to furnish accurate information? Does the underwriter or whomever actually call the owner of each debt that is listed to confirm the current amount and minimum payments?
Before answering, we need to consider context. In some cases, lenders will calculate portions of DTI based purely off consumer-supplied data. Typically, this is for quicker, lower-risk use cases. For instance, you're at a big box store, applying for their store-branded credit card. They aren't going to ask you for five years of tax returns and six months of pay stubs in order to determine your income - they're going to give you a form with a box that says "income" and you're going to write in a number.
However, if you're considering a use case where more risk is involved, there will be more scrutiny. Generally, consumer-supplied data will not be trusted without backup. You mentioned mortgage applications. That's a great example of a case where there is more scrutiny. Typically, in a mortgage application process, you will give the lender permission to pull your credit report. They will use data on the report to calculate the debt side of your DTI. For mortgage applications, the DTI is typically calculated on a monthly basis. Any credit account you have on your report will be included, based on the monthly payment amount shown on the credit report. Since you mentioned credit cards, the monthly payment amount will be the minimum payment due that the card issuing bank reported, on the day that they reported your account to the bureau. So, if you typically carry some balance on your card (i.e. you use it throughout the month), but you pay it off every month, that amount may or may not reflect that behavior. For instance, if you make a few charges and immediately pay them off, you may actually see a zero reported for that card. But if you pay it off once a month, you may see a minimum payment reported, which will be included in the calculation.
Short story: In the case of a mortgage application, for the Debt side of DTI, your credit report is treated as the source of truth.
In terms of income, for conforming mortgage loans (those that meet Fannie/Freddie standards), you will be asked to provide two years of tax returns, plus current pay stubs, as a way to validate your income. It's important to point out that credit reports from the major bureaus do not include income information - so any time a lender wants to calculate DTI with rigorous backup, they will need some proof of income even if they're pulling your credit report.
To address one of your other questions,
Does the underwriter or whomever actually call the owner of each debt that is listed to confirm the current amount and minimum payments?
No, that definitely doesn't occur - essentially, credit reporting exists to alleviate the need to do that.
And, as a footnote, it's worth pointing out a correction to one of your assumptions:
I wanted to make a point that is the OP paid his credit card in full before each month's statement was generated (so that the statement balance read $0) then that is the amount that would be reported to credit bureaus.
That's not inherently true. Card issuing banks will generate bills on a fixed monthly cycle (i.e, your bill may be generated on the 15th and due on the following 1st), and they will generally also send data to credit bureaus on a fixed monthly cycle - but those two cycles don't inherently align (following on the above example, they may send data to the bureaus on the 29th of each month). So, the data that is sent to the bureaus may not exactly match what shows on a given monthly statement.