Template:M gen 2002 ISDA 3(e)

TL;DR: The basic rationale is this:

if the tax relates to the underlying instrument, rather than the Payer’s residence or tax status, the Payer does not have to gross up.
if the tax relates to the Payer’s residence or tax status, then the Payer does have to gross up unless the Payee should have provided information to the Payer which would have entitled the Payer to avoid the tax.
if you’ve agreed the FATCA Amendment, the Payer doesn’t have to gross up any FATCA Withholding Taxes.

The combination of the Payer Tax Representations and the Gross-Up clause of the ISDA Master Agreement has the following effect:

Section 3(e): I promise you that I do not have to withhold on my payments to you (as long as all your Payee Tax Representations are correct and you have, under Section 4(a), given me everything I need to pay free of withholding);
Section 2(d): I will not withhold on any payments to you. Unless I am required to by law. Which I kind of told you I wasn’t... If I have to withhold, I'll pay the tax the authorities and give you the receipt. If I only had to withhold because of my connection to the taxing jurisdiction (that is, if the withholding is an Indemnifiable Tax), I’ll gross you up. (You should look at the drafting of Indemnifiable Tax, by the way. It's quite a marvel). ...
Gross-Up: Unless the tax could have been avoided if the Payee had taken made all its 3(f) representations, delivered all its 4(a) material, or had its 3(f) representations been, like, true).
Stamp Tax is a whole other thing.
As is FATCA, which (as long as you’ve made your FATCA Amendment or signed up to a FATCA Protocol, provides that FATCA Withholding Taxes are excluded from the Section 3(e) Payer Tax Representations, and also from the definition of Indemnifiable Tax. Meaning one doesn't have to rep, or gross up, FATCA payments.