You got some very wrong information. Green card holders must report all worldwide income on their US tax returns, even if the result is that the foreign income does not end up getting taxed by the US after the calculations for exemptions, deductions, and tax treaties are done.
That rule about spending no more than 35 days in the US is the foreign income exclusion rule, but if using that exclusion the income still needs to be reported on form 2555. And even with that rule, there are dollar limits above which you cannot claim the exclusion to avoid US taxes.