A 34-year-old male construction worker from Delhi presents with a 3-week history of progressive pain and swelling over the right tibia. He recalls a puncture wound to the sole of his foot 6 weeks ago while working barefoot on a construction site. On examination, the right foot shows a small, painless scar on the plantar surface; the tibia is warm, tender, and swollen. X-ray of the tibia shows a mixed lytic and sclerotic lesion in the diaphysis with periosteal reaction. Blood culture and bone culture both grow Pseudomonas aeruginosa. What is the most likely diagnosis and the primary reason for this organism's involvement?