True, I was wrong in that.
But it doesn't make a lot of sense to send coins to a sidechain when you are going to have inflation while price is pegged to bitcoin. Holding this sidechain coin will give you less profit than holding bitcoin itself.
Well maybe the sidechain will have more than one native tokens in a way that makes sense. Or maybe a predictable dilution on the value of your sidechain coins might be treated as the cost of buying a certain sidechain functionality.