Ack, please don't. As a manager, I'm pretty sure I'd see this as the bullshit it is and call you on it. We're not all morons.
My boss's goal is to try and get everyone to work every waking hour so we can deliver faster. My job is primarily to keep the peace between the executives and the workers. When I fail the workers, it looks like unpaid overtime. When I fail the executives, it looks like undelivered features.
I think the actual purpose of agile, from a developer's perspective, is to create more time to deliver quality engineering work product. From an executive's perspective, agile exists to squeeze developers into completing tickets faster. As a manager, it's my job to keep both parties as satisfied as possible. If engineers have enough time to build and executives get enough deliverables, then the company succeeds.
What's your strategy?
As I noted in a parallel comment, on my team, developers are never creating tasks on their own or in a vacuum. It's done as a team effort during planning meetings.
Perhaps I should add that my boss (senior director) has never asked me about my board, velocity, or anything like that. Discussion is higher level - "is project X on schedule?" or "are you going to miss anything on your roadmap?" not "why is task X or story Y not done yet?" If your director is asking that, he has too much time on his hands.
Asking specifics from higher ups is just smart.
I've reported to two different directors since moving into management. Both were very clear that they'd rather hear about problems early. And both have been nothing but reasonable when I've reported problems. Of course, the entire team needs to be reasonable for this to work, from the product managers to project managers to individual contributors.
And as a manager, nothing annoys me more than an employee who tells me everything is fine then misses a deliverable. Tell me you're having problems so we can find a solution. Please. That's why I'm paid what I'm paid.