The short answer is No. The extra time these provinces (which also include Ontario and Newfoundland & Labrador) allow you to be out of the province gives you the opportunity to visit parts of Canada, Europe, anyplace else that interests you, in addition to your five or six month stay in the U.S.
But the U.S. law is not changed by these provincial alterations. You are still allowed only six months in a calendar year or the last 12-month period (that pretty well amounts to the same thing) and that law has nothing to do with any Canadian or provincial laws or regulations.
In the past, much confusion has been caused by the fact that provinces allowed their residents six months out, and the U.S. government allowed visitors six months in. But this was purely coincidental and the fact is that these were two separate sets of laws. They still are, and they will remain separate.
At this point the U.S. has no plan to extend the time period Canadians can remain as visitors even though some American legislators keep floating private bills that might suggest such a possibility. It takes a lot to get anything through Congress and this is not the highest priority at the time.
Neither can any provincial government, B.C. or Ontario, force a change in U.S. law, so for the time being understand that though your province may have loosened up its out-of-country allowance for continuation of provincial health benefits, it makes no difference to the American visitors’ regulations—which actually are very generous in that only Canadians are allowed to spend up to 182 days a year in the U.S. without a visa—all other countries are restricted to only 90 days.