To me, the agile movement, at least initially, was about empowering teams to get things done for users. I came out of the Extreme Programming end of things, which had a dozen practices to start with. But the people behind it said that they offered that set of practices as a place to start. From there, teams were supposed to use the short feedback loops to inspect and adapt.

So in my opinion, that is not agile. However, as I've written about elsewhere [1], I think the Agile movement got taken over by something that was more marketable to executives with a top-down orientation.

So in short, I think what they're saying sounds like bunk to me. The way I used points was as purely relative estimates. Point velocity per iteration was a measured quantity, used mainly to make sure the team didn't oversubscribe an iteration. E.g., if the team did 10 last week, this week we'd take on 10. If we thought we might get done early, we could always pull another card in.

But alas, it sounds like you're trapped in what I think of as mini-waterfall, where people who have waterfall biases have broken their big thing down into two-week-sized waterfall lumps.

For what it's worth, I long ago stopped doing estimates entirely except in special circumstances. I now prefer the Kanban-style approach where there's a backlog of modestly sized units of work and the team has a limit of the number of things that can be in progress at once (my starting point is half of the number of team members). You then release each thing as it's done.

[1] E.g., https://williampietri.com/writing/2011/agiles-second-chasm-a...