“AT&T did not file this lawsuit because Verizon’s ‘There’s A Map For That’ advertisements are untrue; AT&T sued because Verizon’s ads are true and the truth hurts.”

So begins Verizon’s (VZ) legal reply to a pair of lawsuits filed earlier this month by AT&T (T) demanding that Verizon pull five disputed ads from the air. The issue: a pair of 3G coverage maps that AT&T claims are “false” and “misleading” and are causing it “irreparable harm” as the two companies enter the holiday selling season.

The 53-page filing lays the factual basis for the ads and concludes its introduction with a  paragraph that gets to the heart of AT&T’s problem: its failure to prepare for the success of Apple’s (AAPL) iPhone, for which it is the only authorized U.S. carrier.

“In the final analysis,” the introduction concludes, “AT&T seeks emergency relief because Verizon’s side- by-side, apples-to-apples comparison of its own 3G coverage with AT&T’s confirms what the marketplace has been saying for months: AT&T failed to invest adequately in the necessary infrastructure to expand its 3G coverage to support its growth in smartphone business, and the usefulness of its service to smartphone users has suffered accordingly. AT&T may not like the message that the ads send, but this Court should reject its efforts to silence the messenger.”

The document is available as a PDF here.

See also:

• The iPhone wars: AT&T vs. Verizon
• Verizon vs. AT&T: There’s a map for that
• Rumors: A Verizon iPhone in 2010
• AT&T Mobility is nipping at Verizon’s heels

[Follow Philip Elmer-DeWitt on Twitter @philiped]