How much the decision to use ternary or binary relationship influences the accuracy of the model with regards to a given business model?

Question

The question title is very long, so here's a little bit of context to (try to) make it clear.

I asked a question regarding ternary relationship. The question was Ternary relationship: what's the difference between having single table and having multiple tables?

It was very well answered by @Michael Green but it raised me another question, which follows.

---

Consider the following ERD:

Consider the following business rules:

1. Companies produce products
2. Companies belong to a sector (examples of sector: machinery, food, software)
3. Products belong to sectors

Questions

• Does the ERD above accurately model the business rules?

• Is there a way to make the ERD very precise regarding the business rules?

• Does the ternary table accurately represent the ERD above? (for that question, please refer to the parent question). If so, then the ERD above is the wrong model with regards to the stated business rules, right?