Hey wheels_up,
I don't think it's an iOS problem. It's our web designers problem. My cousin is a web designer and I had him look at our staff travel ticketing process and he says the site is not designed-formatted properly for use with mobile devices hence you have to come up with these silly workarounds. As if nobody nowadays uses mobile devices eh?
Perhaps a better solution to your problem: on your mobile device, after you enter your email addres and press confirm a pop-up window should appear asking you to confirm if your email address is correct with an option YES or NO. The yes prompt as you said will be frozen because of the sites poor design. However try touching once in any area INSIDE that pop-up window -upon doing so, the page should refresh itself and the pop-up window should reappear centered in your mobile device screen - but this time the YES prompt should be accessible. Try that and it should work. It does for me.
As a former IT major small stuff like this really bothers me. A good site should be user friendly and well-designed on multiple platforms (if not the most popular mobile devices!)
Aloha.