Why does Steve decide against using the Rohypnol?

In The Mechanic, Bishop instructs Steve to perform a hit on another mechanic, Burke. Bishop instructs Steve to slip Rohypnol into Burke's drink, either to cause an overdose, or greatly ease the rest of the operation. Bishop further advises Steve not to engage in open combat with Burke, due to his towering height, strength and experience. He explicitly tells Steve that he should not get into a car with Burke.

However, when it comes time to use the Rohypnol, Steve ponders on it, and places it back in his pocket. He eventually gets in a car with Burke, and travels back to his house. At his house, he tries to strangle Burke, and engages in brutal close-quarters combat with him. When he finally kills Burke, he places the vial of Rohypnol in his mouth - seemingly still in its vial.

Why does he do this? It is clear that Burke is an empowering figure, with a great advantage when it comes to raw strength. We see this in how easily he beats on Steve; Steve is only able to succeed in the hit - and in not dying - through the use of conveniently placed weapons (bottles of beer, a screw driver, etc). Furthermore, why does he place the vial of Rohypnol in Burkes mouth, after the fact? We know that Bishop is training Steven to be like him, and thus an expert in hits made to look like accidents; but surly there is no way of making the bloodied hit look like an accident, let alone via an unopened vial of Rohypnol?