It's not the job of the Government of Canada to out people and corporations who needed pandemic assistance. Corporate filings will require that info to be public. Privacy laws exist, and should be followed. I don't want to live in a rescue shaming country.
If they needed it they would have been eligible (if the programs were made properly). These benefits weren't a free-for-all for anyone to take regardless of reason.
Everyone knew that fast relief meant little to no verification at the outset, as you said. There's also privacy concerns...is it legal to disclose income that individuals are getting from gov? I'm not sure how that works in other programs, like EI, CPP etc.
It's a bit concerning that people like Kevin Page are concerned, he knows far better than us. It seems probable to me that with many people getting benefits they aren't entitled to (by nature of the program) the optics on the gov will be bad so they would have incentive to suppress info.
Knowing how government works in other programs, the amount of effort the gov will dedicate to go after overpayments will be directly related to whether it's in their benefit or not, despite the law. If it costs more to hire/pay public servants to claw that money back than the amount of what they will actually get back they won't bother...unless they're worried about optics of public perception of doing that, which they are (for now).
For other programs like EI and CPP they're decent at going after overpayments, it just might take a long time.