In this type of practice, we are not trying to stop thoughts from coming through. We are trying to develop a gentle, allowing awareness. This means that we are not trying to push thoughts away, or concentrate them away, but learning to develop more awareness. So when the thoughts come through we try to build awareness and objectivity by noting them just as a thought.
This helps us to develop more equanimity and we start to see how thoughts arise and pass, they are impermanent. When we focus our awareness on the breathing, it is not to stop thinking but to develop the capacity to be aware of whatever arises and passes within this focus.
We try to develop a gentle, allowing awareness, which then allows us to see, with investigation, thoughts and the results of thoughts, so that we develop more understanding of the Law of Cause and Effect of the body and the mind.
It is not a problem if thoughts come, it is a problem if we get upset at the thoughts and push them away.
When the thoughts come while concentrating on the breathing, the practice at that time is to develop mindfulness or awareness that this thought has arisen, "thinking, thinking." As we do this and develop more objectivity, we are able then to perceive more clearly what type of thought it is.
The Buddha gave a teaching on what he calls the Five Hindrances, sense desire, aversion, sloth & torpor, restlessness & worry, and doubt. As our ability to be more objective when a thought arises increases, we can then start to recognize which hindrance it is. For example, if aversion arises, we try to note clearly "aversion, aversion." Then we can examine how this thought affects the body. Is there some stress arising in the body and the mind? We use our awareness so we can observe cause and effect which is a law of the mind and body. So we are not trying to just blank the mind, but to develop this gentle, objective, allowing awareness.