OK, let's clarify "snooping". It may mean either that the program says to Windows that it wants to be notified when content on the clipboard changes, or to actually pull the content from the clipboard.
#1 snooping = receiving notifications (and checking what kind of content is on clipboard)
The notifications are used not just for the wizard, but also for enabling/disabling of buttons once you open a file. Basically, if you do anything at all with the program (except just closing it immediately after opening it), it will need the notifications for proper function. Doing what you propose would complicate things (because then I would have to remember whether I have already activated it or not in each place that depends on the notifications being active). Each such added complexity has associated costs. My time is a limited resource and it is not like I can add a feature and forget about it - maintenance costs matter.
#2 snooping = pulling the content
This is not happening. The actual content is grabbed when you click on the wizard or when you click on Paste. Not sure if possibly something else is not pulling the content. There is an embedded web browser on the Online page, which is a Microsoft Windows component. I am not sure how that interacts with the clipboard.