The examples you are giving are simply omitting parts that are obvious from context.
Hey, could you please check [the] MySQL [website/documentation/wiki] for that.
MySQL could be used for the application in general, or the website. Since you can't correctly use the former in this sentence; you can infer that the latter is intended as it is the only remaining possibility.
Context is always key. At work, I could tell a colleague:
Maybe you should talk to a database admin about your this problem?
I don't mean any database admin in the world; I am specifically referring to any database admin who works for the company.
If something is obvious from context (or common sense), it can be omitted.
You can also consider that two separate things can have the same name. This can happen both coincidentally, or because one is based on the other.
How do I prevent this stack overflow from happening in my program?
You should post a question to Stack Overflow.
The casing here reveals the difference, but the principle is the same.
How does Monica Geller know what time it is?
She asks Bing.
Could be referring to Chandler Bing, could be referring to the search engine Bing. Of course, the ambiguity is used for comical effect here, but again the principle is the same.
Maybe a fun bit of trivia that can serve as another example:
Google's algorithm to order its search results is called the page rank. However, it is not referring to "page" as in "web page" (which would be a completely correct and intuitive name for the algorithm), but instead it refers to Larry Page, who created the algorithm.
Alternative sentence, if the website just happens to run, or used to run, on a redhat system.
Hey, could you please see Redhat for that.
I disagree. It is not evident to refer to a website by the system it is using.
Have you checked ReactOS lately?
Facebook runs on ReactOS, but I doubt anyone realized I was talking about Facebook specifically.
There are pretty pictures on IIS, have you seen them?
Although I think OP already knows: IIS is Microsoft's standard website hosting tool.
Not only are you being incredibly vague (many websites presumably run on the same type of system), it's also impossible to exactly know how a website is served to you.
It's not impossible to figure it out if you have the technical skill; but technical skill has nothing to do with communicating in clear English.