Just some thoughts mostly rooted in perception and the aggregate of "others past experiences."

My plumber found out by inserting a camera that my city sewer pipe has roots in it which is causing my house sewer to back up.

I'm rooting for you!

A sewer specialist will inspect the system for you for about $200 and stick a camera in the pipes (drain tile).Drain tile can get damaged for example by roots (Willow trees are really bad and will go a loog way to reach the pipes), but sometimes its just age.The way you deal with the issue depends much on your strategy.

But its guys that live there deep roots.. and can stay right on top of these.. the PM issues are just staggering in almost all cases.

The more you do that, the better you'll get at it but even still most won't sell on first contact.Assuming you found their house D4D, their house is distressed, and it can't be fun and most likely not an accident that they are living in such a state ... they have a problem, figure out how to tactfully drill down to what the root problem is, and if you can present a solution to that problem that is still profitable for you then you can likely make a deal.One other suggestion is to to reframe it not to what they have to lose but what they have to gain.

My biggest lesson was a $7000 unplanned expense when I learned that the entire sewer system under the house was filled with roots so thick that I had to pay for complete replacement from underneath the house to the street. 

She is rooting for me, just as much as I am rooting for myself!!

I again got a plumber out and he unclogged it and found roots in the main pipe from the tree that was cut in the front yard. 

They had an engineer out when they first bought the property about 5 years ago & the engineer recommended a root barrier & gutters.