This is true.

Qualifying for Unemployment Insurance benefits is a decision made by the State, not the employer, and the standard for qualification is much lower than the one used to determine if terminating an employee is legal or not. That is, there are many things that will get you UI benefits that are still perfectly legal reasons to fire someone, as you said.

As an aside, UI is an insurance product sold (forcibly, by the State) to the employer. The employer pays a premium which rises or falls based on the number and cost of claims that employer generates. Naturally, employers are incentivized to reduce the number of claims to keep costs low, but it's not, as is commonly thought, the employer paying benefits directly.

As another side, a strategy companies are using lately to keep their UI costs low is providing a severance package that pays all or part of the employee's salary but paying it out over time. Depending on the state and the rules for that state's UI program, that often counts against any UI benefit the former employee would receive, reducing the weekly benefit (sometimes to $0). It's a thing I've only seen in the past 5 or so years. I would expect States to start to recognize this end-run around the system and adjust the rules accordingly in the near future.