You can use well water or even sodium filtered tap water but don't be surprised if and more likely, when, your plant dies or at the least refuses to pitcher. I didn't think it was important either when I was given my first nep from my uncle years ago. It didn't live long. Neps are expensive so if you look at the cost of using good water or continually buying expensive plants the cost isn't that high!
I will tell you buying jugs of R/O is a PITA if you have a collection like mine, I was bringing 10 gallons home every few days but if you have only one plant a gallon should last you a week or so. At my local grocery store it is $0.39 for a refillable/reusable jug and $0.25 per fill of RO water so if you have only one plant $0.25-$0.50 a week is nothing.
If you have a bunch of plants it may be wiser to purchase a reverse osmosis water purifier. All houseplants, pets, aquarium fish and corals (if you have saltwater tank), and humans too will benefit from the use/drinking of pure water. I got a very inexpensive Reverse osmosis unit from Marine Depot online which will make me 10 gallons of pure water in about 3-4 hours. I can pop the quick attachment on and off the sink whenever I want.
If you have your water tested for TDS (Total Disolved Solids) by your water company and it comes up 90 TDS or less it should be OK but anything over 100 has too much concentrated minerals and matter in the water. Chaska's water registered 412 TDS in January 2003. That translates into over 300% more polluted than it should be for growing Neps. This is likely because Chaska is an old agricultural comminity and the nitrates and phosphates runoff raises the disolved solids content of the water, not to mention all the additives the utilities company adds.
So yes, for good growth/Nep health, quality water is very important, as is bright lighting, high humidity and proper temperatures.