The wording is in my view genuinely ambiguous. Much hinges on "might". The discussion is about what the text best supports.
Two views have been taken of how to understand "might" in this context.
- There will be cases in which the DM can call for a check. And there will be cases in which the DM cannot call for a check. Might in this cases means something like - it might happen that a DM is able to call for a check, and if so they might do so.
- DM can call for a check, but needn't always. Might in this case means it's up to DM.
Proponents of the first view believe that in some cases it is impossible for a DM to call for a check. My stance is that it is always up to the DM whether they decide to call for a check or not, based on surrounding factors (challenges, consequences). This is not to say that I expect a DM to normally call for a check, but our game is very broad - all kinds of circumstances can come into play. So I simply leave it up to DM to manage rules, and players to manage their characters.