As long as one receives his money from a legitimate source, then he can offer the pilgrimage, using that money. It is well known that receiving a gift is a legitimate way of taking money from another person. The Prophet, who was not allowed to take charity from anyone, used to accept gifts. Therefore, there is nothing wrong with accepting a gift which covers the expenses of one's pilgrimage. It is true that some companies and institutions, as well as governments, invite people to offer the pilgrimage at their own expense.
Some companies invite their own employees.
They feel that it is a gesture of kindness or appreciation to the employees to be invited to go on pilgrimage. Some of those employees are reluctant to accept such invitation because of reservations of the type mentioned. Therefore, a company may feel that it needs to encourage its employees to accept the invitation. Obviously, no one forces or pressures another into making the journey. Whether it is better to give the employees money to meet some other needs is a totally irrelevant question.