To my experience, choosing a TL is not "democratic", as it involves evaluations that involve business, dealing with people, communication, attitudes, empathy, organizational skills.
Your colleague was not asking for a democratic process. He was asking to be heard. There's a huge difference. Asking for my opinion is in no way democratic, because my opinion can then be weighted against other factors and maybe those factors weight more, while democracy means all opinions have the same weight. In my opinion, I deserve a Ferrari, but since my opinion has to be weighted against the budget, I don't get one. It's not democratic. The budget wins, it's more important. And nobody really doubts that.
But even if opinions and advice is weighted, asking for an opinion shows that you care. You might not be able to grant all wishes, but you considered them.
Your company did not even consider the wishes of your colleagues. They weren't low on the list. They weren't on the list. The company sent a clear message: we don't care about your opinion. Our decision who to make team leader is not a weighted decision between all factors, including your advice who would be a good leader. No, we sat behind our desks and straight up picked the one we thought best. And it's our thoughts alone that matter. They don't matter more than yours, they are the only one's that matter.
That is one shitty company. I have seen people quit over getting a team lead they did not deem suitable. And not for work matters, they just did not like them personally. Had the company acquired feedback, they would simply made them lead a different team and all would have been happy. But if you don't care and just pull a lazy dictator move, you may see that employees actually aren't just peons. They can leave if they don't like being herded like cattle.
So this is not your mistake. Don't apologize for something you did not do. You do not need to defend yourself, since your colleague was not attacking you with that statement.
But take away a lesson for your own work: you don't need to let people vote. Leading does not mean you need to form a democratic committee every time you make an decision. But a good leader will ask for opinions and then weight all the different factors and make a decision. Not asking for opinions shows that person doesn't actually try to make the best decision by gathering all the factors first, they are just a lazy dictator, not a good leader.