I think there is a general truth to it but the statement is rather simplistic. Thing is yes, I think that if you don't think much of yourself your ability to give to others in any form is hindered. In the case of martyr or overly sacrificial person I feel that what they do for others is not genuine. Due to their own lack of self esteem or self respect I think that on some level they are being generous to others but there is a good chance that a large portion of this generosity and uplifting of others is based on a skewed view and may be mostly obligatory than self sacrificing.

On a certain level in order to truly care and love others -- and all the other things, there is a healthy amount of self sacrifice that is needed but in the case where it is skewed, and the person truly feels less than or lower than others, this is far from a healthy self sacrifice but one that comes from the motivation of obligation, or sometimes neediness by way of thinking in order to get what they need from others they have to do these things.

Also it's worth mentioning that it's a matter of interpretation also. Is this a person that really looks down on themselves in comparison to others or are they just humble? Fine line between the two and really can be interpreted differently by different people.

In summary, yes it is true but there is much more to be said about the subject than just that one line and it's something of a subject that has been studied and pondered for eons.