One thing that makes this issue less prominent is that is happens randomly and refreshing the page fixes the problem. I don't know specific probability of this problem but I would say it happens less than 1% of the time. So when users visit different pages, everything works fine for quite a while until one random moment it stops and they have to refresh the page to make it work again.
In meantime, I found another post mentioning similar issue and the exact same workaround with cache: false.
One more piece of information that might be quite important for jQuery: so far we have been getting support requests related to this problem only from our users who run newer version of our product that users jQuery 1.7.2. So far we have never received such ticket from clients running previous version of our product which runs jQuery 1.4. We were also unable to reproduce the problem on jQuery 1.4. This would suggest that this might be a combination of Chrome and the newer version of jQuery that causes the problem.