Some clarification concerning blue white screening

Hi new to the forum, I was helping my girlfriend out with some homework and what I am reading in her bacterial pathogenesis book is a bit different from what I learned.

Basically, I was wondering how you would use a lacZ reporter to to find regulatory genes that would, for example, that would for example control the expression of a desired virulence gene.

So, let's say I set up a transposon carrying a promoterless lacZ gene and an antibiotic resistance marker such as Kn^r. But how could I use this set up, specifically, to locate genes that would respond to specific conditions or signals?
Suppose the genes that are being sought are expressed at high levels only under low-iron conditions.

I know what is being done here, but something is missing that is preventing me from seeing the big picture. The transposon inserts itself randomly into the bacterial chromosome. When we do our screening at the end by growing bacteria on low-iron plates with kanamycin in them, only those colonies that took on the transposon will grow and show up as blue colonies. However, if the transposons are inserting themselves randomly, how can we possibly tie beta-gal production to upregulation of genes that are only expressed under low-iron conditions? For instance, what if the transposon inserted itself in a region that was directly downstream of murA? Wouldn't this also produce colonies that were blue?

Some help here would be crazy awesome! Thanks for reading and any assistance that you may be able to provide!