They think they can’t live without it. Here’s my proposal on how to deal with it.
Qualitative data > quantitative data
Quantitative data, tracking statistics, is error prone. It can be misleading and it’s almost impossible to interpret the data. You’re dealing with hundreds of various dependencies: tracking implementation, user intent, user reference/source, what the user notices, not understands, what bothers him, what he searches for and (not) lastly but not least: everybody is different.
At best you get an idea of what they do (but not why), at worst you interpret the data wrongly and spend a lot of time in a development/redesign cycle that is useless.
Get real user feedback
Promote user feedback on your site. Integrate it as an important and visible feature of your site. Encourage both negative and positive comments.
Talk to your customers
Talk to your customers when you can. Ask them directly what you can improve, don’t rely on guesswork. Some companies arrange seminars or communicate through other channels like social media. Use them!