Not completely true at all. My kid played town throughout Mite level , took him to an EHF team for Squirts and he made the Elite team. No it wasn't Top Gun or the Bandits or Caps. So it honestly can happen.
Most Elite teams are 90% picked prior to tryouts but there is always room for the 1-2 Elite level kids that just show up, albeit mostly at the younger levels. Also most parents do not tell their current team if they are leaving until after the regular season/playoffs end so needs can change very quickly. Think about tryouts that have 30-50 kids for a total of approximately 26 spots on two teams. The program still needs to fill 13-14 spots on the second team. And yes properly evaluating your kid is important.
Let's be realistic. I believe (unless the team blows up) it will be hard just to show up at try outs. To unseat a current player your son has to be significantly better than a kid already on the team. And to unseat the kid your son only has a limited number of shifts. Given that tryout hockey is not really game hockey, it depends that you kid touches the puck and makes great decisions on these limited opportunities.
So even if the team is not picked, showing up being an unknown quantity makes it so much harder for the kid to succeed during tryouts.
Again, I'm referring to younger ages like mites. It definitely gets harder as they get older.