Refering to this question , Download maps for osmdroid and the accepted answer , on some device it shows blank grid ,though it shows marker ,i kept the zip file of Mobac created tiles in sdcard/osmdroid.
did you add WRITE_EXTERNAL permission in you manifest.xml ?
osmdroid try to catch your loaded map on disk so need WRITE_EXTERNAL permission.
if on some device it work without this permision maybe osmdroid configuration is different or osmdroid folder exist on device.