No I'm not. I grant you it isn't a 1 to 1 and you can break down all kinds of formulas if you want.
The following isn't directly targetted at your point twoNeurons btw, I don't want you to get the wrong idea. I can tell from your post above that you and I are actually on similar wave lengths and you were simply calling to debate the points I made.
As a side note: Fuel is already double taxed just for your records. HST@5% is applied on the price of fuel + all our provincial taxes such as the fuel surcharge, carbon tax, and translink. That doesn't really matter though at the end because when you're comparing 5% to 12% both would be applied on the same amount so ultimately it would still only increase fuel by 7% overall.
On today's taxation matrix for Metro Vancouver I'll save you the math, gas at the pump would go up by around 9 cents a litre if the HST went up to 12% on gas. Fuel for ships, planes, etc., is no exactly the same as how we get taxed for cars (example I don't believe there is a Translink charge on it) but it would still up every litre of gas by 7% meaning cost of fuel goes up by 7%.
Our gas taxes are fixed so you can in essence ignore them.
Anyway...
What my point was is that it would have an increase and that increase would be commulative over time since you pay it over and over vs Mr. Bicycle who has to pay a bit extra tax ONCE.
Let's say for example your groceries you buy every week go up by 2% because of fuel. The average family household (family with 2 kids) will go through around $150-$200 per week in groceries.
We'll take $150 and say that is now $600 per month in groceries roughly. Up that by 2% and you're now paying $612 on groceries. That may seem like a small number but remember it is over time. So in 1 year that is $150 x 52 weeks which is $7800 a year. Increase that by 2% and you're at $156 more now per year that this family has to pay in groceries.
Now I bring us back to Mr. Bicycle complaining about paying full HST on his or her bike. Say they buy a $1,000 bike, a very nice bike indeed, not the best but not the worst. @ 12% HST they are paying $1120 so $120 in tax.
Now let's give this guy a PST portion exemption so his price for his bike drops to 5% HST. Now they pay $1050 so a savings of $70.
So for this guy to save $70 on the purchase of a bike, a 1 time savings I will point out since his bike will probably last at least 5 years minimum, every single family in metro Vancouver will have to pay $156 more per year in groceries.
Thus why I'm saying it is just a selfish non-big picture notion. It would be GREAT to pay no taxes on anything anywhere and get every service you could imagine but the real world doesn't work that way. The unfortunate issue is that BC did exempt bikes at one point of PST so people buying them got used to this fact. Now they're sad that it is gone.
Oh well.
Even if fuel tax increase bumped up prices by only 1% (which I think is extremely reasonable to expect), the family buying groceries in 1 year would pay an extra $78 which is still $8 more than the savings of Mr. Bicycle. In 2 years they pay double. In 3 triple. Multiply that by 100,000 families.
You now have a far greater economic impact than making Mr. Bicycle who is a vast minority unhappy.
Not to mention we have to remember, Mr. Bicycle is ALSO buying groceries.

So Mr Bicycle in a year has basically undone any silly PST savings from buying his bicycle.
People seem to just never look at the big picture when it comes to these things. They listen to the headlines on the radio or read them in the news paper or listen to a random person spouting off a "THE RECKONING IS COMING" style slogan and form an entire opinion on a subject that completely laughs in the face of reality.