I would have to tend to agree, especially in the case that you are working a salary and are receiving the same income, further trading your time for money without the increase of income to justify it. However, it all comes back to your long term goals. If you get paid overtime and feel that it is helping you move towards your goal faster it may be worth it, but I wouldn't recommend doing it simply for an image you are trying to convey to your employer.
As an employee, you are dispensable at the end of the day, however having a strong work ethic and commitment is an invaluable asset to have and you should find a balance between whether your time is worth it or not.
I am under the perception that you should work full time on your job and part time on your fortune - "If you dont build your own dreams, someone else will hire you to build theirs".
RE: Working overtime is probably a bad idea for you