I have noticed the same thing! Most / all native Koreans will correct you, as 수정 did, but you're not crazy!
ㅁ in the initial position indeed makes a sound that is somewhere in between English "m" and 'b". Likewise, initial ㄴ is between English "n" and "d".
If you ask a native speaker to explain it to you, they will tell you that ㅁ always goes "m", and you may even go against your better instincts and try to leave out the hint of 'b' found in words like 못 and 뭐. Don't do it!
I first noticed this years ago when I was listening to my labmate on the phone. I asked her what "deh" meant, and she was confused. Eventually she said, "Oh, 'neh' means 'yes'." I thought I had misheard her on the phone, and that 네 was pronounced "neh". But sure enough, the next time she had a call, I heard her saying, "ndeh...ndeh...".
Why the mismatch between actual pronunciation and self-identified pronunciation? Every human is notoriously unaware of the sounds they're making when they speak. We all have an 'official' pronunciation that we offer when someone asks, and then we turn around and contradict ourselves when we speak.
Easy example: do the "t"s in in 'table' and 'stop' make the same sound? Nearly every native American English speaker will tell you that a 't' is a 't' is a 't'. When explaining how to say 'stop', they may even slow down and aspirate the 't', saying something like 'ss-top." Wrong! American English 't' is aspirated at the beginning of words, and unaspirated after 's'. In fact, American 'stop' sounds just like 'sdop'.
It's the same idea with initial ㅁ and ㄴ. If you're learning Korean, please just copy the way native Koreans speak, and try not to pay too much attention to the explanations.