It all depends on your definition of a telescope.
Digges absolutely built some sort of device that was capable of magnifying objects. It seems that is agreed upon. But the divide is really about whether or not this was a telescope. Some historians shrug it off as little more than a powerful spyglass; others herald it as the first telescope.
There are several accounts that attest to the device's power. Here, Digges' son is quoted as saying
"..... my father by his continual pain-full practices [practical experiments], assisted with Demonstrations Mathematicall, was able and sundrie Times hath by proportionall Glasses duly situate in convenient angles, not onely discovered things farre off, read letters, numbered peeces of money with the very coyne and superscription thereof, cast by some of his freends of purpose uppon Downes in open fields, but also at seven miles declared what had been doon at that instant in private places....."
So it could see things from seven miles off. Here, though, the same quote is discussed and considered mere exaggeration. It does analyze another testimony, from William Bourne:
Yet I am assured that the Glasse that ys grounde, beeynge of very cleare stuffe, and of good largeness, and placed so that the beame dothe come thorowe, and so reseaved into a very large concave lookinge Glasse, that yt will shewe the thinge of marvelous largenes, in a manner uncredable to bee believed of the common people.
This is from a report, commissioned by Queen Elizabeth I, by an independent, outside observer.
The Wikipedia page on Digges ends with this:
However, the construction of lenses to the required optical precision would have been very difficult in the 16th century, and the construction of an adequate mirror would have been much harder still. It is doubtful that Digges built a successful instrument, and the optical performance required to see the details of coins lying about in fields, or private activities seven miles away was far beyond the technology of the time.
So it is likely that Digges built a device capable of magnifying objects at a distance (although probably not seven miles), but it would have been fairly rudimentary, and not much like a telescope today.
By comparison, Galileo's telescope was much more powerful. His first one could only magnify an object 3x, but his final version could magnify an object 30x. That's fairly powerful! A piece of writing 7 one inch tall that was seven miles away would appear to be 30 inches tall. When you think about it, that's a huge improvement. And, after all, Galileo used it to discover some of Jupiter's moons. I highly doubt Digges' device was capable of that!