You are in correct way to find teh problem. You can develop application within latest symbian SDK, but if you want to run that software on early versions you must compile it with that correspond SDK. If no compilation errors occure that sw should be able to install to that older device.
If you use some new API sure you are not able to run that binary in the older device.
Obviously the application should not use some hidden new features...
>>Is this because SDK 2.0 can't build applications for version6.1 phones
Yes ! you must always re-compile within 6.1 and hope the sources are compatible.