The thing at the bottom is not a York white rose. The design of the York rose is quite consistent. It isn't merely "a flower with white petals". In particular,

The thing at the bottom is not a York white rose. The design of the York rose is quite consistent. It isn't merely "a flower with white petals". In particular, these always have five petals; the one at the bottom has six. Not every white flower is a symbol of York versus Lancaster.