Make room for the other version
Ask what the other person understood before assuming that you are arguing about the same facts. For a message about how to reconnect with a former intern, use this factual base: remind the person where you worked together, when, and what current topic makes the contact relevant.
Correct the record precisely
Correct only what you can support, acknowledge any real impact, and propose a practical way to prevent repetition. Make one modest request and give enough information for them to decline or redirect it. Make the immediate next step clear enough that the recipient can answer without reconstructing the entire history.
Agree on a testable next step
Do not imply endorsement, exploit a former hierarchy, or send confidential material from the old relationship. Use official business, privacy, conflict, and procurement rules when commercial or regulated information is involved. Do not recruit an audience, publish private evidence, or turn a misunderstanding into a campaign about character.