No. Surprisingly, there is an adaptive immune system in prokaryotes. This is still widely unknown. The newest review is
S. Al-Attar, E. R. Westra et al: Clustered regularly interspaced short palindromic repeats (CRISPRs): the hallmark of an ingenious antiviral defense mechanism in prokaryotes. In: Biological chemistry. 392, 4, April 2011, 277–289. doi:10.1515/BC.2011.042. PMID 21294681. (Review).
Cited from abstract:
Many prokaryotes contain the recently discovered defense system
against mobile genetic elements. This defense system contains a unique
type of repetitive DNA stretches, termed Clustered Regularly
Interspaced Short Palindromic Repeats (CRISPRs). CRISPRs consist of
identical repeated DNA sequences (repeats), interspaced by highly
variable sequences referred to as spacers. The spacers originate from
either phages or plasmids and comprise the prokaryotes' 'immunological
memory'. CRISPR-associated (cas) genes encode conserved proteins that
together with CRISPRs make-up the CRISPR/Cas system, responsible for
defending the prokaryotic cell against invaders.
An application of the CRISPR/Cas system is the immunization of
industry-relevant prokaryotes (or eukaryotes) against mobile-genetic
invasion. In addition, the high variability of the CRISPR spacer
content can be exploited for phylogenetic and evolutionary studies.
Despite impressive progress during the last couple of years, the
elucidation of several fundamental details will be a major challenge
in future research.