To answer your question as you have asked it.
Yes, anyone in a completely silent room can here a very low level white noise if they pay attention.
That said, there are a number of causes of actual tinnitus, if you were to have it, that would need to be ruled out.
These would be ear/hearing a number of causes here...so ENT.
TMJ, Cervical spine problems.
A problem with the small bones in the ear.
Tumor [usually loud and one sided].
To me, it sounds like you have something not to worry about, as your doctor said.
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