Sometimes, and I am of course not an attorney, it might make more sense to use outside contractors for some repair issues. In my experience, I have done this just to protect my maintenance team, one, from being treated like idiots, but mostly I do it because, two, the company is protected as contractor assumes all liability. I have used licensed plumbers when Residents act like that for things like water heater replacements and difficult shower diverter/leak repairs. I have also used heating and cooling contractors for A/C and furnace issues when I have repeated "knowledgeable engineers" who just KNOW that the air temp is plus or minus 3 degrees different from the thermostat reading. In 100% of these issues, using the contractor shut the resident up and in 75% of the time the Resident renewed.
However, I would get out there and sing the praises of the Maintenance Tech by posting all the tasks he/they complete: like posting notices on facebook, etc. about what a great preventative maintenance program you have - they just changed all the air filters, furncace filters, outside lighting inspection completed, powerwashed the buildings, etc. I would also ask Residents you know and trust who feel the techs are GREAT to post testimonials on Google, your website, facebook pages, etc.
Finally, I think it is unfortunate that she endured a night without water. If this was the case and I knew the Resident was going to be inconvenienced (any resident) I place them in the Model or a hotel at our expense. Who can complain about that? If the Resident has family nearby and wants to stay there, then I would comp the day of rent plus give her a Visa Gift Card.
I am not sure why you are responsible for the work of those who are no longer with the company. If residents call in a service request and it is completed within an acceptable time frame, you have held up your side of the lease terms. But, maybe an attorney would say different.
The one thing I would NOT do, is place her routine work orders above someone else's. The suggestions I have made are for all residents, not just your distrusting, complaining ONE.