Your boss is right. Usually, ice consists of nearly pure water. The supernatant contains the buffer salts and other reagents. Hence, the concentration of your reagent will be higher than expected. Partial freezing of aqueous solutions can be used to concentrate a diluted solution, and the other way around is used to desalt sea water.
On the other hand, if you are working with biochemical reagents, frequent freezing and thawing might reduce the activity of your reagent. It is better to aliquot your solution and do not freeze it again.