The TDS might not even be required, before it becomes a credit problem
Section 9(1)(ii) only pulls salary into India's taxing net when the services are actually rendered in India. If your role is genuinely performed from the US, day to day, that salary sits outside this deeming provision on India's own domestic law. Layer the treaty on top and it gets clearer still: Article 16 of the India-US DTAA gives the country where the work is physically done, the US, the primary right to tax it, with only a narrow short-stay exception that doesn't fit a founder running the company full-time from abroad. TDS still gets deducted anyway because an Indian company paying "salary" defaults to Section 192 as a matter of habit, not because anyone actually checked whether it was owed.
Once it's deducted, US law can refuse to credit it
Assume the TDS happens anyway. The next assumption, that a US foreign tax credit absorbs it, is where the second failure sits. Under IRC Section 861, compensation for services performed physically within the US is US-source income, full stop, regardless of who paid it or from where. The US foreign tax credit under IRC Section 904 is limited to the US tax on foreign-source income. If the US treats your salary as its own US-source income, the Indian tax you already paid on it isn't foreign tax on foreign income from the US's point of view, and the credit formula can simply exclude it. You end up having paid India tax that wasn't clearly owed, on income the US won't let you offset either.
What goes wrong without a CA
The recurring pattern: the Indian company's payroll or accounts team treats the founder's salary exactly like any resident employee's, Section 192 TDS deducted by default, because that's the standard process and nobody flags the services-rendered-abroad question. The founder discovers the gap at US tax filing time, when their US preparer can't fully credit the Indian withholding against the US tax on the same salary. By then, fixing the classification doesn't recover tax already paid; the fix that actually works is getting the position right before the next payroll cycle, not after a year of returns are filed on the wrong assumption.