If there is no particular cause for the depression as you say, like a severe trauma or psychosis, and there is not an underlying condition that may require being treated with a combination of talk therapy or CBT and medication, such as bipolar disorder, I can’t imagine why this psychiatrist is saying such a thing. Your child definitely needs and deserves a second opinion.
I mean, there are more than three categories of anti-depressants, so he hasn’t even tried all the CATEGORIES of anti-depressants (SSRIs, SNRIs, MAOIs, tricyclic antidepressants, atypical antidepressants, and then those that fall in the “other” category - that’s six categories) much less considering the numerous, numerous different anti-depressants in each category, of which there are probably 100 or more, all together. Perhaps Google which of the categories he’s tried (put the name of the medication he took in Google, and when you find it on Wikipedia, it will usually tell you in the very first sentence on the page, such as, “Venlafaxine, sold under the brand name Effexor among others, is an antidepressant medication of the serotonin-norepinephrine reuptake inhibitor (SNRI) class”). Then you’ll know which categories haven’t been tried. Not to mention if he discusses with a thorough psychiatrist, they might determine his low moods might also be affected by social or life-stage anxiety, or some combination? Often, some people need a combination of anti-anxiety and anti-depressant medications. It’s difficult to say.
But to say there is no hope from medications after only trying three is almost negligent, and really not on, of that doctor. Please tell your son not to give up.