The Jewish standpoint is that this is a legend used to support the reason why Jews (and other Eastern tribes) have reservations about taking a census.
According to ancient Jewish superstition (yep, we got them in our culture just like others), a census can bring evil upon the people counted. It's not really known why we Jews have this superstition (some other cultures do too). Rabbinical sources and folklore connect the taking of a census to the cause of all types of problems, from national disaster to making a person susceptible to "evil eye"!
Yeah, I know. It's ridiculous, but we Jews used to believe that. Some believe it is because our G-d told Abraham that his children would be "like the sands of the sea, unable to be numbered," and thus holding a census is seen by some as tantamount to challenging the Almighty G-d. Exodus 30.11-16 even declares that in order to avoid "plague" each person enrolled in a census has to pay G-d for his protection from such adverse effects.
Our ancestors saw their fears and superstitions as intertwined with their religion, so it takes some knowledge of the culture, its quirks and its failings, to tell what the Jews were sometimes saying in the Scriotures...and sometimes even that helps but little.
Unlike the JWs we Jews don't claim we know for sure what is happening here, but like many things about Hebrew (like reading right to left), you need to read the story differently than with the approach many Christians take with it. Apparently there was a national tragedy which the Jews couldn't explain due to the ancient belief that G-d protects his people from all adversity no matter what. Yet when disaster did strike it left people looking for a reason.
What caused it? Hmm, nothing...the people were being faithful, they were showing allegiance to the King, and the King had just finished his census, and--
WAIT! The census!
So, according to genre, a narrative was devised that states how God sent a plague due to David's census, for as you know 'taking a census causes all kinds of evil!'
There's a lot in Hebrew writings of all types that you have to approach this way. There are genre earmarks that are common to legend, myth, or parable. Because the Jews never expected their writings to be read by Gentiles, they didn't write with other cultures in mind. Superficial readings caused by religions like the JW remove the texts from their intended audience and paradigm, and read in a vacuum where the demand is that everything written has to be fact causes nonsense.
Not that it makes too much sense to the modern Jew either, but at least we don't run around saying this is factual history and condemning others if they don't believe in our interpretation.