I was lucky in that I was dealing (in both cases where I've run similar flows to this) with above-board exec teams who wanted the best quality information I could give them - even assuming that estimates are just assumptions - even if it meant having some tough conversations about scope or headcount.

Good managers / business leads/ execs / champions CAN be reasoned with, as long as you find common language, think and understand their priorities, provide alternatives that meet their underlying goals (all of which frequently falls on the presenters). E.g. in your situation, it may be that unspoken expectation was to cut scope or increase resource contour or find another way to meet deadline rather than just changing estimates; or something completely different.

Occasionally though, you're as you say stuck between other people's indecipherable politics. I find in such situations, I'm most comfortable speaking the most honest truth and working hard, openly and explicitly, to understand/ask/bring to surface everybody's actual critical goals.