No idea what your employer's negotiated rate includes or what the rate you found does and does not include, but it is pretty common for negotiated discounts to still cost more than the cheapest possible rate. That is because some companies want LDW or other features and that may jack the rate somewhat.

Needless to say, if you are paying out of pocket and have the choice between the use of a corporate rate for personal leisure travel for others and a lower rate, you should choose the lower rate if it includes the features you want.