There is a very old doctrine called the Mystery Doctrine, which according to some, the GB still believes, although they haven't printed anything on it for decades. According to this doctrine, the anointed are "the Christ." Under this view, the anointed (who used to be the FDS) were very much the same thing as Jesus himself.
This thread from Terry is worth re-visiting:
http://www.jehovahs-witness.net/watchtower/scandals/278783/1/APRIL3d-MEMORIAL-3d-Time-to-review-the-Mystery-Doctrine-secrets#.U3Tkh9JdVj8
Regardless of whether or not this is still official doctrine, at a minimum you get a flavor for why people often get the general feeling you describe.
Here's an excerpt from Terry's thread:
Writing in his book, "Apocalypse Delayed" Penton tells us:
"The Mystery, as understood by Pastor C.T. Russell, meant not only had Jesus offered himself as a ransom sacrifice for mankind, but the body of Christ, the 144,000 members of his church also participated in the ransoming and atoning work" [pg 40]
He went on to say :
"Pastor Russell divined the mediator for the New Covenant was "the Christ" and that expression meant the 144,000 actually participated in Christ's sacrifice for the world" [pg 187 of "Apocalypse Delayed"]
Going back to Russell’s day, the original idea was a distinction between "Christ," who is Jesus, and "the Christ," which is composed of Head (Jesus) and Body (all spirit-begotten Christians).
In Rutherford's day, those who partake of the bread and wine belong to "the Christ" and who share in the glory of Christ (the mystery doctrine).