As I understand it the Alberta Fund is completely controlled by the province. There is some national policies, especially with exports, that falls under the Feds, but how much (or little) flows into the Fund is completely up to the province.
It is on Alberta itself that it decided to have low/er provincial income taxes and no provincial sales tax. Those things were 'funded' by the resource revenues, which effectively came a sort-of cheque to the habitants of the province. And when oil prices went down, government funded went sideways.
IMHO Alberta shouldn't blame Ottawa for not setting aside something for a rainy day.
The big example is the National Energy Program which (aside from its economic impact on the province) basically tainted politics in Alberta and probably contributed to their hesitancy to contribute to a fund which could potentially be raided by the Federal government in the future.
This is Alberta we are talking about? If in your hypothetical the Federal Government didn't mess it up the Province would.
* https://www.fraserinstitute.org/fr/node/9227
And they're not the only ones to be positive, as Ontario has had several surpluses or small deficits ($200M):
* https://en.wikipedia.org/wiki/Ontario_government_debt
This of course assumes that a balanced budget (or surplus) is something that even should be aimed for. Certainly one shouldn't go crazy with spending (especially when stimulus isn't needed), but the balanced idea seems to be a strange fiscal fetish that is over-focused upon.