Let me give examples of questionable vs. approximate:
A reliable source such as the New York Times reports a certain person
was found on the streets at the age of about three and the best estimate
of his birth date is July, 1990. This is approximate.
An infamous tabloid reports a certain celebrity was born October 9,
1940, the same day as a well known musician. The article goes on to make
many highly speculative comparisons between the two celebrities. The
date is not approximate, but it is questionable due to the dubious
reputation of the tabloid.