B737-800 Captain reported communications issues complicated a maintenance related delay that led to an aircraft refusal.

Narrative

I was Captain (CA) and operated Aircraft X on Day 0 from ZZZ1 to ZZZ. Was running about one hour 15 minutes late due to a maintenance procedure. Arrived in ZZZ to operate flight ZZZ-ZZZ2 and proceeded to the gate. Passengers had already been boarded and the Agent meet us at the gate. The Agent said that everything was ready and they were just waiting on us to depart. I greeted the number one Flight Attendant (FA) and gave them a FA brief; made a passenger announcement and proceeded to preflight the cockpit. The First Officer (FO) performed the walk around came back and said they had bad news. The FO then showed me a series of photos of a very large fluid trail from mostly the right main gear well and some from the left main gear that propagated all the way back to the tail skid.Based on the photos; it looked like a very large leak of some fluid. There were still some spots where you could see a shiny sheen; which indicated fresh fluid. We immediately notified maintenance and I wrote up our findings in the logbook. A Mechanic met us in the cockpit and then took the logbook and said they would inspect the situation. A few minutes later; the Mechanic came upstairs and said it was hydraulic fluid; and they were going to have to inspect further. I then called Dispatch to inform them that we potentially might not be taking this airplane and if there was a Plan B to maybe consider it. The Dispatcher said there's a possible other aircraft available if we were going to cancel at this time. I said not yet; we were going to give the mechanics time to inspect and tell us what they found. A short while later another Mechanic entered the cockpit and asked if we would assist them with running the flaps up and down while they verified and/or looked for any leaks. We agreed and discussed how we were going to perform this with the Mechanic. With maintenance assistance; we deployed the flaps twice. The Mechanic then returned to the cockpit and stated they did not see any leakage at this time. I also shared with them our findings on the hydraulic fluid quantity level. The Mechanic stated that they would need to look further to see if they could find anything. But as far as they're concerned right now; it looks OK. We asked the Mechanic to step outside and we talked between ourselves and determined that a quick look late at night with a couple of mechanics and flashlights at night would not be enough of a determining factor in our opinion based on the size of the leak that we noticed. We agreed that we would not accept this aircraft for safety reasons. We immediately notified Maintenance; Dispatch; and the Agent of our decision. Dispatch said to remove the passengers. I confirmed with the Agent and informed the FAs and made a PA to the passengers of our situation and to deplane. A Maintenance Supervisor entered the cockpit and asked me to sign the logbook stating that we were refusing aircraft which I did. We then asked what was going to happen to the aircraft and they stated that it was going to go back to the hangar and they would swing the gear and do some other inspections to determine if and where there was a leak. Crew scheduling called and advised us that we were released to the hotel. After the passengers had deplaned the aircraft; we secured the cockpit; and as we walked by the gate podium; a visibly upset passenger with tears in their eyes approached us; and stated ' Captain if you refused this aircraft for safety reasons; why are they going to put us back on it and send it to ZZZ2'. The FO checked the computer and confirmed that this aircraft was to be utilized to ZZZ2. I inquired with a maintenance person; and they said the aircraft was airworthy and they were going to use this aircraft for that flight. This upset passenger also indicated that the Gate Agent had told them that we (Pilots) refused the aircraft and then waited long enough to time out. I assured the passenger that Company personnel wouldn't put the aircraft in service if they didn't feel it was airworthy; and that the information about us delaying was inaccurate. There were several upset passengers in the gate area over this information. This was a potential public relations situation. This could've been handled by the agent 100 different ways just by choosing better words. A new flight crew was assigned to operate this flight and that Captain also refused this aircraft for safety reasons.