I immediately thought of the Zimmerman telegram, when the article stated the Telegraph Office had had a relatively quiet WWI. Which led to a quick bit of Googling to refresh old memories.
It's interesting how things was different back then.
Britain cut German cables so as to force them to broadcast by radio, so we could crack their codes. And also to be annoying.
Comms discipline was pretty poor back then. Codes weren't all that good, or rigorously designed. And lots of stuff got sent in the clear. One reason the Germans trounced the Russians so badly in Poland and East Prussia in 1914 was that the Russian HQs kept issuing orders by radio with no encoding whatsoever. Also the German High Seas Fleet did their internal communications by radio when in port! Rather than by runner or ship-to-ship cable, which couldn't be intercepted.
The US offered the Germans some telegraph help. Take uncoded messages to their embassy in Berlin, and the US would re-transmit them over their "secure" lines. Said lines went via Cornwall for amplification, and so were sneakily copied by the British. *Ahem!*
The Germans managed to persuade the US ambassador to send the Zimmerman telegram in code - well they couldn't exactly get the Americans to transmit their plans to pay Mexico to invade them could they? Awkward!
So the British government spent a few months looking for plausibly deniable ways to get this to the US, without admitting spying on their diplomatic traffic or that they'd broken the German codes.
Which made it harder to say it wasn't an evil British forgery. But then Zimmerman went and publicly admitted it was genuine anyway! Despite German diplomats in the US and Mexico trying to say that it was a Britihs fake. D'oh!
Also, what a stupid idea! Mexico was only just (mostly) stopping its own civil war. How the hell did the Germans expect them to be able to conquer Texas and New Mexico? Even if they were a united country there was no way they were going to be able to beat the US army, and it was obvious that they would know that too. So why make the offer, and risk Mexico telling the US about it and bringing them into the war quicker? Unrestricted submarine warfare was likely to bring them into it eventually anyway. It's a strange old story...