There are different levels to reading.
The first level is like knowing the alphabet and how the letters sound. You can recognize the notes on the staff, but you have to sound out each chord. You cannot recognize "words", or in this case, chords.
The second level is like knowing the shapes of words. When we read English, we don't have to sound out the words because we recognize their shapes. I'm sure all of us have seen the jumbled word test, wehre yuo cna sitll raed teh wrods enve thuogh thye'er mixde, which is like reading chord inversions. This applies to reading sheet music: once you can recognize the different shapes of the chords, then you don't have to sound it out.
The third level is when you can recognize groups of chords, and internalize it before you actually play it. This is called chunking. We do this when we read English too. Good readers can read groups of words before they say them aloud.
The fourth level would be like speed reading. Expert readers can internalize huge chunks of words. An expert sight reader can look over sheet music once, and play it without ever looking at it again.
Personally, I fall between level 1 and 2. I used to be at level two, but lost it when I stopped playing for five years. I haven't put a lot of effort into gaining it back yet. I'm between 3 and 4 with my ear, because I can hear the quality of chords and progressions, and sometimes even repeat a song perfectly. Because of some gaps in my knowledge, I feel I'm still an intermediate player--maybe even a low intermediate.
A lot of people here will say they are intermediate, when they're really beginners, or say they are advanced, when they are really intermediate.
I'll give an example:
I bought a bottle of "Banana Cream Muscle Milk" yesterday. My daughter saw it and wanted some, but when I asked her what it was, she hadn't seen the bottle, and thought it was juice. This is what happens when a beginner hears a song: they don't even get close to it.
After she had seen the bottle, she could read the words but couldn't sound out "muscle" correctly. She said "myuscal". My wife and I laughed, but she didn't think it was funny. She also saw the banana image, but from where she was sitting it looked like a lemon, I guess. An intermediate player is like this: they can play the song pretty close, but it's still off a little.
An advanced player cannot only create music, they can also replicate what they read and hear.