I have heard of no such requirement. If you are the author of code that merely depends on MIT-licensed code, there are basically no requirements on you that I am aware of.[^1]
You would have to do those things if you published, say, a fork of MIT licensed code, or if you copied a substantial piece of the code directly into your code base. Basically, the portion that you copy remains MIT-licensed even when it appears in a private codebase, and this must be communicated at least to people with access to that private source (not necessarily to end-users), usually via a code comment.
This is in contrast to the GPL, which affects all code that depends on the package. This gives the GPL a viral nature, and is why I avoid it when possible.
[^1]: Looking at the precise wording, it is unclear whether monomorphizations of generic functions defined in an MIT-licensed crate count as portions of “the software;” but the way I’ve always understood it to mean, that would simply not be in the spirit of the license.