A Lady's Guide to Fortune-Hunting question

For me when she first had this discussion with Radcliffe I was confused how easily she gave up. I thought she would try to challenge him before reluctantly giving in, especially when she found she was having no luck I found it hard to see why she respected Radcliffe so much despite actually having no loyalties to him. I think it was actually through fear of people finding out about her standing that she unwillingly felt defeated and moved on. But what I find it hard to understand is why did she not just deny it more so? How could you prove this or was she certain that nobody would listen to her over him? If she had waited for Archie to become of age, she could had ran away with him and still secured enough money.