There's a lot more to the story than this, but it sounds a lot like "Cantata 140" (1964) by Philip K. Dick, published only in The Magazine of Fantasy and Science Fiction, July 1964.
The point-to-point transportation devices are called "'scuttlers" and are described as grey-walled tubes. The original inventor, Henry Ellis, found that he could look out from the tube and see tiny people who spoke ancient Hebrew; other people have found that they can access other, secret, places through the cracks to hide.
Historically, the original defective 'scuttler had belonged to an employee of Terran Development named Henry Ellis. After the fashion of humans Ellis had not reported the defect to his employers... or so Rick recalled. It had been before his time but myth persisted, an incredible legend, still current among 'scuttler repairmen, that through the defect in his 'scuttler Ellis had—it was hard to believe—composed the Holy Bible.
The principle underlying the operation of the 'scuttlers was a limited form of time travel. Along the tube of his 'scuttler—it was said—Ellis had found a weak point, a shimmer, at which another continuum completely had been visible. He had stooped down and witnessed a gathering of tiny persons who yammered in speeded-up voices and scampered about in their world just beyond the wall of the tube.
Who were these people? Initially, Ellis had not known, but even so he had engaged in commerce with them; he had accepted sheets—astonishingly thin and tiny—of questions, taken the questions to language-decoding equipment at TD, then, once the foreign script of the tiny people had been translated, taking the questions to one of the corporation's big computers to get them answered. Then back to the Linguistics Department and at last at the end of the day, back up the tube of the Jiffi-scuttler to hand to the tiny people the answers—in their own language—to their questions.
A description of the 'scuttler in operation:
He entered the big gleaming circular hoop which was the entrance of the 'scuttler, found himself—as usual—within a gray, formless tube which stretched in both directions. Framed in the opening behind him lay his work bench. And in front of him—
New York City. An unstable view of an industriously-active street corner which bordered Dr. Sands' office.
You can read the story in F&SF at the Internet Archive. The story was later expanded into The Crack in Space (1966) (Wikipedia plot summary) which carries the story further into what happens when the government tries to open the alternate world lines to colonization.