I'm not entirely sure it's always billed as 10% of full fare. Last year (pre-merger), we flew DEN-TLV on (what were then) XC awards for two seats, with lap child... the lap child fare came out to about $400, but I'm pretty sure that the full C fare for that route was more than $4K. I could be wrong, but I think that $4K was the cheapest available C fare, and they billed me 10% of that, not 10% of the full fare.

I should note that we changed our flights (dates and routings) about 6 times (these were using 1K miles so no penalties), and the price always stayed within a few tens of dollars of that, so this wasn't an issue of one misinformed agent... every time the rate desk looked at the lap child ticket, the price came back similarly. But, again, maybe $4K was the full C fare... I just don't remember that to be the case.

So... hopefully you'll have a similar experience and be charged 10% of the lowest available C fare, rather than full fare.