@rbl
Check the manufacturer's recommendations for cleaning and sterilizing your equipment when in doubt. They've tested their equipment and know what their equipment can handle. Pay attention to replacement times. If it says replace every 3 months and you are cautious, do that.

If using distilled water in a baby bottle sterilizer there is no need to sterilize first. The baby bottle sterilizer will do that for you while sterilizing your equipment, as long as the cycle is over 5 minutes. I believe most of them are, and average between 8-13 minutes of steaming time.

The reason to use distilled water with our equipment has to do with mineral build up. Period. Spring water from your filtered system it seems will still have minerals (which our bodies need for drinking). That said, mineral buildup takes time to build up. You probably will replace your equipment before it becomes an issue.

The nebulizer I use is sensitive as it contains a metal mesh head. Manufacturer says to boil for 5 minutes in distilled water, so that's what I do. Replacement heads are expensive, $125 so I take good care of them. Sprint LC and Aeroeclipse nebulizers are much less expensive and are made of all plastic making them conductible to microwaving. 3+ minutes in microwave with spring water is fine. Look up manufacture instructions and follow them.

Remember that most of the cautions we read about originated around those living with cystic fibrosis, a very very vulnerable population.