The problem is, even if this is what the intent of the line is, we are left with the problem that everything we know about transporter technology as of that film suggests that Enterprise's transporters not working shouldn't prevent Kirk from beaming aboard. Starfleet must have a few dozen working transporters at least, and even if for some reason the ground transporters couldn't beam him up to a ship, the transporter room on the Orbital Complex certainly should.
Actually, to that point in the series, which is basically just TOS, had we ever seen a fully-functioning transporter room that wasn't on a starship? I remember seeing receiving pads at a ground location or two, but no independent beaming from such places (or even visible controls for independent beaming). It's possible that beaming from a planet-based location wasn't practical in those days, whatever the technobabble reasons.