Okay, I ride a Hybrid bike generally but also use a road bike.
Now, if you haven't gone to the bike store yet,
Back problem is a common problem with road bikes.
There really is something about how your weight is distributed on a bike and where your seat/saddle is positioned at, high or low.
I think you want more lean on top of the handlebars as that takes more weight off your back.
http://www.spine-health.com/conditions/sports-and-spine-injuries/bicycling-and-back-pain
Bicycle Lab:
http://bicyclelab.com/bicycle-saddle-pain-and-discomfort/
(Video)
Notice how the gentleman's seat is higher so more of the weight is distributed leaning towards the handlebars. This is exactly what you are talking about.
I do think with some bikes, hybrids that are upright like the old 3-speed bikes, the back pain problem is more rare.
Also found this, since I started stretching, so many pains I use to have, have seemed to have gone away. Stretching like this or even Yoga: