An individual company sets its prices to optimize revenues. That depends only on the demand curve and is independent of costs. However, it's a rare market where even the most marginal suppliers earn enough producer surplus to make up for significant increases in production expenses. If the optimal revenue isn't enough to turn a profit then the business will close. That decrease in supply with no change in demand allows the remaining suppliers to raise their prices—though not necessarily by the full amount of the increase in cost, because only part of the decrease in supply manifests as an increase in price. The rest manifests as potential consumers doing without the good altogether, perhaps turning to lower-priced (but less satisfactory) substitutes.

That’s not what they say when the subject of tariffs comes up. “We’ll have to pass it on to consumers”.

But in reality, a share of the tariff is paid by the supplier and a share is paid by the consumer.

And if I remember my classic macroeconomics class correctly, that share depends precisely on the elasticity of demand (slope of the demand curve).

This is correct.

Economic facts pay little heed to economic rhetoric.

Companies only ever tell the truth of course.

This is unequivocally false. A 3% increase could make their costs higher than revenue. They would increase their prices or go out of business.