It is what the Greek manuscript literally says. I read NT Greek.
I am not sure about the Greek, but in any case, as Robertson notes, the binding and loosing is repeated by Jesus to all the disciples (Mat.18:18). Later after the Resurrection Christ will use this same language to all the disciples (Joh_20:23), showing that it was not a special prerogative of Peter.
See also Clark on Mt. 16:19: http://live.e-sword.net/app/
No doubt the apostles, being part of the foundation of the church, exercised binding and loosing power in both doctrine and discipline. Paul, as an inspired writer, which Rome is not, taught believers are loosed from the ceremonial law, (Col. 2:14-17; cf. Gal. 4:10) as does the writer of Hebrews (Heb. 7-10) and which was also confirmed by the church, (Acts 15) as a fulfillment of the New cov. And in 1Cor. 5, Paul, together with all the church, binds a man in discipline, and Peter declares that a man is in the “bond of iniquity.” (Acts 8:23)
This is in contrast to Rome loosing herself from needing Scriptural warrant for all her teachings, and loosing upon men teachings not found in Scripture (from her virtual bottomless well of “tradition”), and binding people from freely reading Scripture and imprisoning, torturing and killing such as differed from her (which early Prots were also wrong in doing much the same, having yet to unlearn that from Rome).