Is a DC to AC Inverter safe for Laptops?

I'm trying to figure out if a DC to AC power inverter is safe to use with my laptop.  (I have read some other posts that suggest building a DC to DC convertor and skip all the inefficiencies, but I am still curious about this....)

I bought a 350W inverter to use in my pickup off the cig lighter to recharge cordless tool batteries and my laptop.  The inverter won't charge my laptop with my truck engine off as it 'resets' for low voltage after about 15 seconds.  (Note: Laptop AC to DC converter puts out 150W DC and has an input of 225W AC)  When the truck is running it is fine.  I thought there might be a problem with the inverter so I checked the output voltage and it was ~ 96VDC.  I checked a buddy of mines (in my truck with the same meter) and it was 110 VDC.  I was guessing I didn't have a true RMS meter after checking my inverter, but now I really don't know what to think.  I understand that the 60HZ output from most inverters is a modified square wave and not true sinusoidal like household AC.  Will this modified square wave have a destructuve effect on the AC to DC power supply/chargers for my tools and laptop?

If I'm going to destroy something, I'd rather take the time to build Dc to DC convertors.