The Form 8833 (which you correctly note is not supported by TurboTax), page 3, is referring to the waiver of the requirement to use form 8833 to report the treaty position and is not a waiver of the requirement to report the income on your tax return. You will need to report the income, and the taxes paid on it, to get a credit for the taxes paid to your country of birth.
Since I don't know which country's treaty you're reviewing, it's a bit difficult to say with certainty from excerpts alone, but it sounds as if you aren't required to use Form 8833 in order to claim credits for foreign taxes paid.
To claim the credit in TurboTax, you have to enter the income in two places.
First, enter it either in the entry area for Form 1099-R or Miscellaneous income. The Miscellaneous income area is a bit easier when you plan to electronically file your return, but has some limitations particularly if you file a return in a state that may reduce the taxes paid specifically on pension income.
Next, enter the income in the area for Foreign Tax Credits. The income reported in this area doesn't go on Form 1040 as income, but is used only on the Form 1116 to aid in determining your tax credit. Only the first entry (1099-R or Miscellaneous income) will report the income on your Form 1040.
If you're not required to file Form 8333 (because of the waiver), then reporting the income and the subsequent tax paid for the credit will take care of your reporting requirements.
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