Yes, I'd agree with Lukas about this.
'Bring on' is most used for health issues, and it is often something that might have occurred anyway. If an old person suffers from rheumatism, for example, this can be brought on by damp weather. Midwives can give expectant mothers drugs to 'bring on' labour if they are late in delivering.
'Bring about' is indeed less immediate, and refers to a more complex cause and effect situation, and a more complex set of conditions - such as the events which trigger a war, or the debate as to whether global warming has been 'brought about' by fossil fuel use. You couldn't possibly use 'bring on' for those situations.