The uncertainty in how many people would be saved anyway without intervention is (as an absolute number, not a percentage) much larger for the 250000 people case. If someone claims to save 4500 people, and the uncertainty is greater than 4500, I may be skeptical that they can save anyone at all.

Imagine it as medical trials instead. If I claim I can cure 4500 out of 250000 people it may be that I can't cure anyone at all and I'm just counting the spontaneous remissions as "cures". If I claim I can cure 4500 out of 11000 people, it's very unlikely that they would have all recovered spontaneously.