Appendix W - Child visa refusal

Here is the background:
My wife got her Tier 2 - General visa.
But since her SOC is "2211 - Medical practitioners", even the dependent is required to submit a criminal record certificate from all the country that I had lived for more than a year in the last 10 years.
I was not able to apply for Tier 2 dependent as it takes few months for me to get criminal record certificate from Japan. My daughter applied for "Appendix W - Child visa" but it was refused since only 1 of the parents had applied for Tier 2 visa.

As a Japan national, my daughter (as well as myself) can enter UK without a visa for up to 6 months.
Any idea if my daughter will have any issue since her visa application has been rejected?