USB current draw and CE marking
CE marking and USB standard are completely different to each other. CE is for safety, USB is functionality. So this is at least two different questions.

No idea what the factory is quoting the 1A limit for CE. Ask they for what standard this breaks, they should know, that's what you're paying them for. CE is a lot more worried about EMC, EMI and voltage limits rather than a current value. Assuming you've done a good design, EMC and EMI should be fine (and they'll give you a report of emissions), and USB is 5V (unless you're doing some of the higher power chargers).

As for the current question about USB, no rules are broken if you don't claim to be USB certified. But be aware, many users don't know about current out of USB, so will claim your device is broken when it doesn't work. This is why the Amazon Echo comes with a dedicated USB supply, as they clearly state that you have to use their USB supply due to the higher current capability of it.