Day 1's are a nightmare, that's why I always prod mods to put in clues and mini-games for day 1. If it makes you feel better I think everyone hates Day 1. I know I do, shoving games forward on day 1 has contributed to making me a routine night action magnet, NK target, and perpetual suspect #1. Admittedly it is not the only reason but it is a big factor in it. There's a very direct correlation between player activity and night action usage.

Instead we lynched Beet, who was a scummer. Walking the razor's edge is half the fun of the game, for me anyway.

But it isn't random at all, the logic is simple. We lynch people, on the surface, for scummiest behavior, but ultimately our goal is to try to nail the scum while expending the minimum assets. A good townie tries to aim as many bullets at the scum as possible while minimizing the odds of a townie dying and minimizing the damage to the town. This is why a vanilla Day 1 claim is considered anti-town, it does not help the town because it is either true or it isn't, if true it gives the scum better odds of killing a roled player, if false then we have to activate the Lie-Lynch policy. So anything that harms the town's chances at victory is anti-town, and anything that enhances it is pro-town, and in the absence of a good specific suspect the town has only 3 options:

1) No Lynch - but most of the players consider this to be anti-town
2) Random Lynch - But a true random lynch is anti-game, it is just tossing a die.
3) Minimize possible damage to the town by selecting a target who is as likely to be scum or roled as anyone else, but if town is acting in the most anti-town or least pro-town fashion, minimizing damage to the town.

There's more to play then role powers, we need investigation, deduction, insight, prosecution and defense, etc and those can only be observed via what people post, more we know that the scum are most strategically aided by silence. Even I consider it so, I just consider silence anti-game and don't use it, but it definitely is advantageous. So silence by a townie aids the scum because it allows them to minimize their own risk by matching it. The scum who prefer to be talkative typically are steering the mood and agenda anyway, and having done that a lot I can say it is much easier to do if other people aren't out their trying to steer and object. When many players are quiet then some of the scum can hide form sight and exposure and the stronger ones can steer the ship. So silence is anti-town and thus not a 'random lynch' at all. Not just because it minimizes losses but also because it often prods players into action.

It's important to understand that as frustrating as Day 1 is for townies, it is more so for the scum, this is their most powerful yet most vulnerable time. Every question, every line of attack, has a chance of toppling them before they've been able to meet and speak. Whole lines of future maneuver can be clipped out by a single remark from a scummer on day 1 even if they survive un-lynched and unsuspected. The clever scum get together on night 1 and create a grand plan and fallbacks and means of warning each other covertly during the day, they can act as a group and find each other's overlooked errors or messups. But not until night 1. They're weakest now and that's why pressing hard on day 1 is vital.