B737 Captain reported refusing the aircraft because of a misapplied MEL that did not address a bleed duct air leak near the keel beam.

Narrative

I refused the Aircraft X. Agent 1 came to the flight deck to ask me and FO (First Officer) about exactly what the issue was so he could explain it to the very angry Passenger. I gave him a very detailed description as to the issue why I was refusing the aircraft as it sits. Same agent came by later to advise me they were swapping me with Captain Name on Aircraft Y going to ZZZ2. FO advised me at that time he was not going to fly Aircraft X as it sat either. All my Flight Attendants also advised me they did not want to fly Aircraft X as it sat as well. FO and myself went to the next gate to talk with Captain Name. As we arrived to Captain Name's Aircraft Y; Agent 1 walked out of the flight deck. Captain Name listened to my reasons why I refused Aircraft X and Captain Name agreed based on the facts that he would not fly Aircraft X as well. Captain Name also stated that he could not believe Maintenance Control actually put in writing in the System; that there was a bleed air leak near the keel beam unaddressed and let the plane fly for X days. Crew Scheduling then put my entire crew back on to Aircraft X. FO and myself were then removed and put into reserve. Duty pilot refused to speak with me and said to call Name1. I called and got no answer. My FO was told by Crew Scheduling that the Crew Scheduler heard that we refused Captain Name's aircraft as well because it also had an APU bleed issue. I NEVER even thought or mentioned this to any body; but it appears an agent in ZZZ called Operations saying I would refuse Captain Name's aircraft. I in fact told that Captain Name I absolutely would take his plane. It's not about not having APU bleed. Captain Name also mentioned that he was told that I wanted to 'steal' his aircraft until I supposedly found out the bleed valve was also bad; and then I was going to refuse his aircraft as well. Upon leaving the gate area; 2 of my flight attendants mentioned that they were interrogated by at least 2 agents. All 4 Flight Attendants spoke proudly of me and my actions as well as my FO. The posted delay for this flight stated that I refused to fly the aircraft and left. Same for my FO. Myself and FO remained either on board the aircraft or in the gate area for several hours until released by crew schedule on an assignment. The Aircraft X delay code only mentioned the fact that we refused to fly Aircraft X. Not mentioning the airworthiness of Aircraft X. Another fact that was also conveniently omitted in the delay code; was that Captain Name as well refused to fly Aircraft X in its current condition. Another convenient omission on Aircraft X; Captain Name flight delay message; was the fact that his flight was initially; substantially delayed while station personnel and crew schedule attempted to convince Captain Name to take my Aircraft X. The ramp closure delay noted on his flight was anecdotal at best and not representative of the actual delay. The Aircraft X was finally flown to ZZZ1 by Reserve Captain Name3. 'Trouble Shooting' was performed; with no other action mentioned; and MEL reapplied to try to convince Captain Name3 that Aircraft X was airworthy. No positive corrective action of any kind was performed before Aircraft X departed almost X hours late. The duct leak or duct damage; was still there; no damage inspection was accomplished and the MEL was still inappropriately applied to the APU bleed valve.Upon arrival in ZZZ1; Aircraft X was taken out of service. Maintenance Controller Name5; the same maintenance controller that approved the release for Aircraft X to depart ZZZ; requested to re-open my log entry after Aircraft X got to ZZZ1. It is worth noting that my [log entry] was not written completely or correctly into the pilot report portion in the computer system. Here is my AML entry correct and in its entirety: Crew refuses this aircraft due to the following issues. APU bleed air was operating correctly prior to deferral. Maintenance confirms in tracking system there is a suspected bleed duct leak near the aft cargo area. A suspected bleed leak in the vicinity of the keel beam was not inspected for bleed air leak damage. The confirmed/suspected bleed air leak is presumed to be stopped by the APU bleed check valve. There is no MEL relief for this. Under the original incorrectly signed off AML entry; it shows that a duct and clamp was finally replaced late in the evening on Date1.Cause - Maintenance Controller attitude on keeping metal moving; degradation of Captain's authority. Increased ethics.Suggestions - Increased ethics....