I'm wondering whether the real reason is actually that the RNA polymerase during the transcription doesn't stop immediately at the end of the protein encoded by the gene, but continues until it falls off the strand in either rho-dependent or independent way.

This is certainly a possible reason. Others:

• 5' and 3' untranslated regions
• non-coding RNAs
• polycistronic transcripts

As Mensur Dlakic noted, bacteria have 3 and 5' untranslated regions like any other organism. The polymerase absolutely doesn't stop at the end of the protein coding regions. This is well known. Note, its not just that this sometimes happens, but it is the norm.

Its also that case that bacterial genes are transcribed as cistons (again, as noted by Mensur). Cistrons are single transcripts that contain the coding sequence for multiple proteins. Again, this is the rule, rather than the exception in bacteria.

However, its also worth noting some other explainations.

Firstly you dismess genomic contaimination, but you shouldn't - no DNase treatment is 100% effective, and your intergenic signal is much weaker than, say, the signal at the gene at the left of the plot you show.

Secondly, polymerase binding and transcription initiation is a stochastic process. It happens at all points in the genome at some low level. If you sequence deeply enough you will find transcription from any part of a genome.