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.