I think @dmertz meant to say that the IRA custodian has no way of knowing whether your contributions were deductible or not.
Remember that when you make out of pocket contributions to a traditional pre-tax IRA, you have the option (depending on income and other factors) of taking a tax deduction. If you took a tax deduction for your contributions, then all your withdrawals are taxable now, because you didn't pay tax on any of the money before. This discussion only applies if you made contributions to a traditional IRA and didn't take the tax deduction.
If you made non-deductible contributions to a traditional IRA, then you created a form 8606 that year. Every succeeding year when you made additional non-deductible contributions to a traditional IRA, you would use the information from the prior form 8606 and your current tax return to generate a new form 8606. This is how you keep track of non-deductible contributions, and it is your responsibility to keep a copy of your most recent form 8606 until you start making withdrawals. When you withdraw from the IRA, if part of the IRA contributions were non-deductible, you will use your most recent form 8606 to calculate what part of the IRA withdrawal is non-taxable. That adds a new form 8606 to your tax return and you keep that form (always keep your most recent form 8606) and use it every future year that you make withdrawals until the non-taxable portion of the IRA is used up.
You have to keep track, and file the papers with the IRS to prove part of the withdrawal is non-taxable. The IRS doesn't do this for you, and neither does the IRA plan.
