"Is the satellite image always right?" Defintely no.
Note what we tend to call "satellite imagery" is actually taken from aeroplanes and needs to be georeferenced and corrected for distortions caused by viewing angle of the camera and varying elevation of the ground (hills, mountains etc.).
Depending on well this processing is done, the imagery can have errors around dozens of meters down to a sub-meter range. Note that this can change substantially even over short distances. For example where I live Bing imagery is quite good (sub 1m error), 10km away from here Bing has errors of over 30 meters.
The only way to determine if the imagery has an offset in the immediate area you are working on,is on, is to compare it to other sources. For example:
- GPX tracks
- Objects that have had their coordinates determined with high precision
- Objects that have been imported from high accuracy sources (for example French cadastre data)
Once you have determined if or if not the imagery has an offset that is large enough to need correction at least Potlatch 2 and JOSM allow you to adjust the position of background imagery.