You have the same log history in git as you do in Svn - a linear chain of commits. What you describe as a tree is due to the branching and merging. SVN has the same thing, you branch just as much as you do with git, the difference is how the 2 store this information internally.
eg where I work, we use feature branches for independant development. Then the final fixes get merged to the product release branches and trunk. Not too dissimilar from how you tend to use git.
I worked at a place that used git (alas, not me, I was in the Windows team and had to use TFS :( ) and too many people used ot have to call the git guru over because they would munge up their repos. I don't know how they did it, but the fact that they did it too often for my tastes suggests git is a tool that is only for advanced, or experienced users only. Unfortunately that means nowhere near enterprise development.
Today, I'd never suggest git, I'd go with Fossil if I needed a DVCS.