Abstract and link to subject paper:

http://www.habitablezone.com/space/messages/554275.html

If we ever get our interstellar migration act in gear, we won't have to
worry where Earth is over the next few million years.

By the way, if you read the paper carefully, the author is not saying
that our planet's trip through the galaxy is uneventful; it is more that
there is still plenty of missing data on past events to be certain whether
or not dipping up and down through the galactic medium has any kind of
major effect on Earth or not.

Unless we ever build a time machine, I have a feeling that a lot of data
from many millions of years ago will remain missing. Unless we one day
run into an ETI that recorded what happened to the Sol system since
the Precambrian and shares the data with us.