Here is some info...
Student ticket allotment is about 21k.
There isn't a "lottery". Student tickets are sold on a first come, first served basis. When kids were still allowed to sell to whoever they wanted to, tickets were selling out too quickly, some that bought them were turning around and trying to sell them immediately for a huge profit, and you had a lot of pissed off kids and parents who didn't get tickets. So, the athletic dept switched it up and took control of the resale market to eliminate the scalping.
You can sell your tickets for games that you don't want to attend (assuming that someone wants to buy them). The complains that many have is that you need to do it by the day before the game, and that there is a "floor" on the price (ie you can't sell it for $5 or $10 like you could in the old days for crappy games).
There wasn't an issue with student not "flagged as passing external security". The issue is that they got into the stadium without an actual ticket (usually, they swipe IDs and are given a ticket to their seat). Because of opening the gates to relieve the pressure, the students didn't stop to get a ticket, and thus weren't let into a section because they didn't have a ticket for that section.
And it's not about "multiple security checkpoints". It's all about the wanding. The "wanding" is a slow process, and they don't have enough "lanes" to handle volume like 10k students showing up within 20-30 minutes of each other.
It's complete horse$hit that they "regulate" the resale market - students should be able to freely exchange their tickets to other bonafide ID-baring students. Claiming that a student buying a SINGLE season-ticket for "scalping / profit" purposes is beyond ludicrous and would be equivalent to PSU telling general season-ticket holders that they are not free to exchange their tickets as they see fit! (actually worse, as season-ticket holders can purchase entire blocks of tickets if they wanted to do it for scalping / profit purposes!). Essentially students are buying a "restricted class" of ticket, but there is NO REASON whatsoever that PSU needs to be a "middle-man" when a student (who only controls one ticket) wants to exchange their ticket-right to another bonafide student.....complete horse$hit that the University gets in the middle of this "exchange". If they have such massive "excess demand" in the Student Section, they should sell more student tickets, not restrict the rights of the limited tickets they sold!!! That or sell unlimited student season tickets and make them worthless if unused (i.e., non-transferable) and limit seating to the first 25,000 students that present credentials on any given gameday (it would also encourage students to find their seats earlier)......if you are going to effectively make their rights worthless if they aren't going, this would be a far better way to do it.