I know what you mean, I've heard it like that too.
I heard some people say it's because your tongue is in the same position when you say 네 and 데 so those sounds are similar, and same for 미 and 비 if you try it out yourself.
You should remember than 네 does not 100% equal 'ne', that's just a close English representation of the sound to make it easier for English speakers to learn it. But it is not an English sound, it is a Korean sound :) So maybe sometimes it might sound somewhere in between 'ne' and 'de' but there is no English letter for it.