Help, XDF-S12-T20 , "with..."状语 or 定语

isuffering

20. In December of 1987 an automobile manufacturer
pleaded no contest to criminal charges of odometer
tampering and agreed to pay more than $16 million
in civil damages for cars that were test-driven with
their odometers disconnected

(D) having test-driven cars with their odometers
disconnected


In analyzing the structrue
"having test-driven cars with their odometers disconnected",

some one explains that  

"have" means "有"
and
"with ...." modifies "cars" as 定语.

But I think that
the structure is "having done sth with... "
and
"with ...." modifies "having done sth " as 状语

Looking forward to your discussion.
Thanks in advance.