Link: https://www.youtube.com/watch?v=-HZrTUNJKCs

I came across a sentence from BBC English at work, and it is:

Let's remind ourselves of the phrases he suggested Anna uses when negotiating a sale.

What I've learned is that with the verb, suggest, you can only use either 1) suggest + infinitive verb or 2) suggest + ing, as in

1. He suggested (that) Anna (should) use these phrases.
2. He suggested using these phrases to Anna.

So isn't the sentence from the BBC grammatically incorrect? What have I got wrong? Thank you in advance.