It seems pretty clearly there is a disconnect between different areas of the company you have interacted with. Not surprising in a large company, and also not surprising that everyone in all areas is not up to the minute on every potential candidate who is interviewing or wants to find a position. This is assuming you didn't actually interview or have conversations with this specific person as part of your interviewing process.
So this senior person who also does outreach has contacted you, based on the fact that you are the lead of your school's consultancy society.
You tried to join the company, and jumped through a lot of hoops that they require for people trying to join up, but as soon as they decided you weren't for them, they stopped communicating and basically treated you like a number.
I think it's fine to tell this person exactly that -
"I had a bad experience with you guys, where your communication process for applicants was inconsiderate, so I'm not comfortable giving you access and an endorsement for my group." This will lead to discussions with him, and maybe some inquiries and apologies, but, even if that happens, I wouldn't change my stance, once taken. That would only undermine you as the leader of the group, if it looked like it was based on personal pique.
As irritating as it is, and, perhaps, not being worthy of your seal of approval, it still is, sadly, more common than not with companies. With the ease online application and the sheer volume of applicants, most HR departments have "we'll only contact you if we're interested or still interested."
I don't think I'd trash this company on any sites, specifically, based on what is standard practice.
However, that caveat is quite different for someone who has already been involved in a lengthy process which, I assume, includes interviews and interactions beyond application. There's really no excuse for going radio-silent to someone that far in the process.
Definitely tell this guy "no," but only give a negative review or comment on networking sites after very, very careful consideration. If you read such a review from someone else with a similar experience, would it come off as a legitimate warning you'd appreciate, or would it come off on sour grapes or entitled complaining?
Make sure you are deciding from as objective and non-personal a space as you can.