Here in Europe being fired "for just cause" does not impact unemployment benefits but does require quite the standard of proof (it's can't be just done on "your performance evaluation was not high enough", and the company has to, for example, prove that somebody stole from it) but they can then avoid paying compensation. Also firing without just cause (i.e. laying off) is not generally possible outside the trial period unless in exceptional circumstances (say, the company has provenly been losing money and hence is firing a fraction of its employees).
This does vary from country to country and is part of the basic employment law, so in places with strong Unions it's even more strict.
So this kind of situation in this video does not apply because to fire for cause the burden of proof is on the company, not the employee: she cannot be just fired "for cause" merelly because the company claims the underperforms.