Player A can indeed re-raise in this spot.
The rule of only calling would apply if the SB had pushed all in with an "under-raise"... ie not enough to complete a full raise.
so, say player A calls the 1000, then the SB pushed all in for 1500.... the BB has not yet acted so would be allowed to make a raise, however when the BB just flat calls, Player A only has two options - fold, or call the extra 500 to match the SB"s under-raise.
hope that helps...
