It's easiest to see how a wormhole can be anchored to a planet by considering so-called "thin shell" wormholes.
The mouth of one of these is the same as its throat. [In its most symmetrical form, it would manifest as a spherical boundary between two regions of space. If you were to stick your hand through it, your hand could be thousands of light years away from your shoulder. (One assumes approximate spherical symmetry -- there's at least one hole punched through the thin matter shell through which travelers pass.)]
The matter in the wormhole's throat could be charged, in which case it could be anchored with an electric field.
If this matter is fermionic, it would obey the Pauli Exclusion Principle, and could therefore be anchored by physical constraints composed of fermionic matter -- e.g. an anchoring net.
The wormhole's throat matter, despite being negative, would still be attracted by the planet's gravity. However, the planet would be repulsed by the wormhole's matter. If it's a tiny communication wormhole (big enough for, say, a laser beam), this repulsion is insignificant. It it's a man-sized wormhole, the repulsion would exceed the attraction of any planet whose mass is less than about 1-Jupiter mass.
Despite a great deal of effort by physicists, there is currently no theoretic proof of the non-existence of wormholes. When quantum theory is considered, negative energy becomes theoretically possible. [Of course, it's also theoretically possible to reverse the rotation of the galaxy.]
It is also possible to engineer a wormhole that has arbitrarily small gravitational effects (these are called "absurdly benign" in the physics literature). Also, wormholes need not have event horizons. Although the cost of not having one is negative matter at the wormhole's throat.
Lastly, evidence is not required for rational belief in the existence of a phenomenon. Belief can be justified by a well tested theory. For example, there is no evidence for the existence of gravitational waves. But nearly all physicist believe that they exist. This was much like the widespread belief in the Higgs particle before its discovery in 2012.
Source: The Physics of Stargates -- Parallel Universes, Time Travel, and the Enigma of Wormhole Physics, by Enrico Rodrigo (2010)