A false premise. If that were true, just like you stated, we wouldn't support it. Actions speak louder than words, and all that.
EDIT: I realize I sound far more judge-y than intended in these posts. My overall point is that people should just do whatever makes 'em happy while doing the best you can (w.r.t. everything else). Trying to emphasize the morality in your actions is just wrong, imo.
Taking the child labor thing into account, never being brand new electronics again would pretty much take care of that. One could make an argument that buying used goods is still supporting child labor, but I'd argue it's a sunk cost.
Why choose this example? Child labour is rife in many sectors, particularly textiles.
It's also rampant in electronics recycling[0]. So even if you never buy any new electronics, you're complicit when you dispose of your old electronics.
The point is you shouldn't allow an impossible quest for perfect ideological consistency and moral purity to prevent you from doing good on a imperfect, inconsistent scale.
[0] http://pulitzercenter.org/reporting/india-rising-tide-e-wast...