It is the responsibility of the purchaser to remit provincial sales tax for a purchase made from another province.
Both GST and HST are federal taxes, with a portion of the HST being sent back to the province after being collected by the feds.
Federal tax is non negotiable, and must be paid regardless and is collected by the retailer.
Some retailers, large ones, charge PST because they have a business license in the province you reside in as well. (Cabella's, WSS, etc.)
I only know this because I collected signatures for the "Stop the HST" campaign, in BC, which will either have you hate me or thank me.