Will battery replacements with more power hurt the system?

[bof]

My laptop came with a six cell battery rated at 11.1 V, 4800 mAh with a 
3.0 hour life. When I went to buy a replacement from the manufacturer, 
all I could find was an eight cell battery rated 14.4 V, 4800 mAh with a 
4.5 hour life. (No one else in the country seems to be making 
replacement batteries for this system, so it would seem that I am stuck 
with the manufacturer).

When I asked their Tech Support if the higher voltage of the eight cell 
battery would hurt the computer, I was told it could damage the computer 
and to make sure that I used ONLY a six cell replacement.

When I pointed out that the eight cell battery was being sold by the 
manufacturer as a replacement, and that in fact they also offered a 
twelve cell replacement, I was then told that the larger-celled 
batteries would not hurt the system, just give a longer life. (It should 
be noted that the larger-celled batteries cost much more, also).

So which is it? Will the additional power of the larger-celled batteries 
hurt anything or not? It would be nice to have a longer life for the 
system, but not if the higher voltage is going to hurt anything.

BOF