B737-900 Captain reported disagreement and failure to follow procedures during a maintenance delay. The aircraft was subsequently removed from service after the Captain declined to remove a valid entry from the log book. The aircraft was swapped and the flight continued with another aircraft.

Narrative

This report is intended to highlight a serious safety culture concern with our interfacing Maintenance Control partners in ZZZ - Aircraft X/737-900ER. Operational pressures and logistical concerns were present which resulted in the flight crew being excluded from Maintenance actions; along with being put in a position to accept a seemingly unairworthy aircraft.Upon arriving at the gate; the aircraft was en-route to the terminal as a tow-up. The flight was already delayed three hours. While conducting the walk around; I observed a significant amount of Fuel Dripping from beneath the Right Engine. I can appreciate that this could be due to cooler temperatures and seals contracting given the time of year; however we had some time prior to departure and it was a greater rate of fluid drip than I was comfortable with (approximately 3 drips/second). Furthermore; it was not particularly cold outside; so it presented differently than normal cold weather-related fuel drips.Once I got back to the flight deck; the First Officer (FO) pointed out to me that the accumulator was below 1;200 PSI. This seemed low despite the FM pre-flight value of 1;000 PSI to contact Maintenance (FM XXXX). To give us more SA on the status of the Parking Brake Accumulator; I pressurized the Hydraulic System and then turned the pumps back off. While the brake pressure did go up to approximately 3;000 PSI (normal); it depleted quite quickly and got to the 800p PSI maximum in about 3 minutes - well inside of the 30 minute FM limit (FM XXXY). Having experienced similar in the past; this was presenting as a possible accumulator pre-charge leak. A report entry was made for both the Fuel Leak (LP# XXXXXXX) and the Accumulator Pressure anomaly (LP# XXXXXXY).Maintenance Control responded to the flight deck and stated that they needed the flight deck to move some actuators. The First Officer and I vacated the flight deck and proceeded to the jet bridge. At this point; the aircraft was almost fully boarded; it became incredibly loud on the jet bridge like that of an aircraft parking next to you. However; there was not an aircraft parking next to us - it was our mechanics motoring the Right Engine. I immediately went to the flight deck to inquire as to why an Engine was being run with Passengers onboard and I was told that they were motoring; not running it because they were not introducing fuel. In my available source document information (FOM XXYY); running an engine for a maintenance purpose without fuel introduction is not really defined. Yet a safety risk does exist with Ground Personnel moving around an aircraft (especially a delayed one).Shortly thereafter; the Technicians came out of the flight deck and stated that the leak subsided with the engine motoring. There was a subtle assertion made; which I did not appreciate; about writing-up engine leaks because we get paid to run them. I can assure you that the add pay associated with an engine run DID NOT factor whatsoever into my decision to write-up the original fuel leak observed during the walk around.Upon reentering the flight deck; the Technician stated that he was going to sign off the Engine and for me to reject the accumulator write up (or Cancel reports in ACARS). I asked why and he stated that it was good to go. I asked if he was going to take the time to sign off the Engine; to which he responded in the affirmative. So I said that he could then do similar with the accumulator if it was truly good to go. He then; again; said that I could just also reject the write up. To which I said I would not and that he could affirm its operational status through signing off the accumulator report entry as an Ops Check Normal. He then reminded me that it was shift change and all it would do would further delay the flight. I did not acquiesce and stated that we would wait for shift change to occur. Given the time reference to shift change; we were also left to wonder if the Technicians were really able to conduct the engine run procedure with passengers onboard or if they did not want to be delayed at the end of their shift.With the new shift in place; they determined that the pre-charge was quite low and had to increase it through a maintenance procedure. There was then a leak check that had to be performed. Again; the accumulator bled down to the maximum and; albeit within the tolerance; the Technicians further troubleshot. They confirmed that the accumulator was not holding its pre-charge and further investigation was warranted. As a result; the aircraft was taken out of service and the flight subsequently canceled due to no spare aircraft available. It is further important to note that the original report entry was ultimately cleared by a change of the entire accumulator assembly.