Again, besides the Enterprise sling-shotting back to the 1960's, they had Gary himself ride in on a beam that's probably capable of time travel. They said so.
Well, to be clear, Scotty offered a theory that the beam "could've brought him back through time,"
but he was simply guessing--probably due to another advanced being (other than themselves) suddenly appearing at the same point in old earth history, when he assumed (due to a lack of knowledge) that no humans time travelled in the 20th century. Taking all into consideration, I do not believe the script suggested time travel was any true
ability of Gary Seven (or his commanders).
I disagree. I believe we have to interpret the line in the context of a backdoor pilot. "Could have brought him back through time" equals "we're going to leave our options open for time travel episodes on our spin-off". It doesn't mean that it will be used that way, but rather really to make it clear that Gary can pull literally anything
out of his hat that the Enterprise
can do, time travel included. Otherwise, why even feed us the "theory" in the first place.