Should Statutes be Interpreted in Light of Regulations?

A partial answer from the Nova Scotia Court of Appeal: yes.
In McIntyre v. Nova Scotia (Community Services), 2012 NSCA 106, the applicant's spouse had received a lump sum pension benefit, which meant that she had received an "overpayment" of benefits.

There was no doubt that there had been an "overpayment" within the meaning of the statute. But she pointed out that her spouse had received the overpayment, not her.

That would have been a winning response had the implementing regulations not defined "chargeable income" as including the income of a spouse.

In the absence of any challenge to the regulations themselves, the applicant was out of luck:

[58] To summarize, I disagree with Ms. McIntyre’s submission that the Regulations are irrelevant.  Section 3(f) says that an “overpayment” means  assistance that should not have been paid “according to this Act and the regulations”.  By Regulation 47(1)(a), Mr. Leblanc’s income is “deemed” to be income of Ms. McIntyre.  That establishes the definitional condition for an “overpayment” within s. 3(f).

It seems like an unfortunate story from Ms. McIntyre's point of view. She won, unrepresented, before the first-instance administrative tribunal, but this decision was quashed on judicial review. She then changed lawyers for her appeal. Her most recent counsel was allowed to make additional arguments on interpretation, but did not (and presumably could not, without leave) challenge the lawfulness of the regulations themselves:

[23] Had Ms. McIntyre submitted that the regulations were ultra vires the Act, that issue would be of central legal importance, not within the particular institutional expertise of the Board, and would be subject to correctness review.  Ms. McIntyre does not suggest that the regulations are ultra vires.  Her submissions are purely interpretive.

Mind you, even correctly interpreted, the regulations were probably intra vires.

From Ms. McIntyre's point of view, though, it must be infuriating that a government agency would wait for many months before notifying her that she owed them over $6,000, and then expend many multiples of that amount on legal fees.