Bernard Williams defined equality as an equal state of all people or striving for an equal state if the latter is absent at the moment. Nobody can decide whether one group of people should be treated in a different way than another; no one moral principle can be applied to explain the fact that some groups of people should be treated unlike others. From this standpoint, Williams argument claiming that the doctrine of negative responsibility erodes personal integrity is rather ambiguous.
To understand whether this statement is true or false, one should clearly find out why a person did not act or failed to prevent something. If an individual did this on the grounds of his/her moral principles (which are established by culture and religion), then it is simply immoral to hold him/her responsible for the consequences of not acting and failing to prevent something. In this case, personal integrity would be really undermined since a person would be unfairly blamed for sticking to his/her just and fair moral principles. If an individual does not act somehow and fails to prevent something by means that do not infringe upon his/her moral values, he/she should be held responsible for such actions since indifference is not permissible in our world. Under such conditions, the idea of personal integrity would not be undermined because a person is blamed not for sticking to his/her moral principles but for indifference.
Taking into consideration the things mentioned above, it can be reasonably claimed that it is still possible to be a utilitarian and respect the integrity of individuals. For this purpose, a utilitarian should realize the idea of general equality: all people are equal and deserve the same degree of happiness. If one person discards his/her projects for the benefit of others and becomes unhappy because of this, overall happiness is diminished. Thus, utilitarianism can be justified only if personal sacrifices lead to universal happiness/benefit not only of the majority but also of a person who gives up something for the sake of others.