need help on translating sentence from manga

this sentence is something that the main character fujinuma thinks to himself after having a conversation with his manager. fujinuma is only a part time worker, but the manager wants to offer him a full time position. however, he is indecisive since he is also striving to become a published manga artist as well.
フラフラしてるように見えるって事の裏返しの言葉でも あるんだろうが。。。俺みたいな奴に有難い言葉だ。。 。

the only part I am having trouble on is how to interpret 裏返しの言葉 and フラフラしてるように見える. フラフラ means to stagger or be unsteady on one's feet, so my rough translation of フラフラしてるように見える is "he (the manager) seems to be unsteady on his feet".

i couldn't make sense of 裏返しの言葉 so I tried interpreting the entire phrase フラフラしてるように見えるって事の裏返しの as modifying 言葉 instead. 裏返し means inside out or upside down, so my rough translation of フラフラしてるように見えるって事の裏返しの言葉 is: "the words that show the opposite of the manager being unsteady on his feet".

so the manager doesn't seem to act like he really needs fujinuma that desperately?

am i getting this interpretation right? help will be greatly appreciated.

フラフラしてる doesn't refer to his appearance or the condition of his body there. It expresses his current state of life "to live aimlessly" or "to have no regular employment". (He actually has an aim, but his manager doesn't know it, right?)

thanks for the reply!

so フラフラしてる is referring to fujinuma rather than manager. then i think i can interpret フラフラしてるように見えるって事の裏返しの言葉 as: "the words to turn over my seemingly aimless way of living". this seems to make more sense than what I had earlier.

would this be a more accurate interpretation?

裏返し means "another side of the things" in that case.

うらがえし【裏返し】
II 〔物事の反対の一面〕
彼の横柄さは劣等感の裏返しだ
He acts arrogantly because he 「suffers from [has] an inferiority complex.

Click to expand...

裏返しを英語で訳す - goo辞書 英和和英

Thus, the manager says the words because Fujinuma seems フラフラしてる to him(= manager)

I wasn't aware that 裏返し could be used like that. I understand the sentence much more clearly now. thanks for your help!