So, what exactly is GCHQ (or Theresa May) saying here? Are they implying that the Five Eyes pact has been changed since 2013 to ban using intelligence sharing to circumvent national laws, or are they (implausibly) trying to deny that such circumvention ever occurred at all under the original terms of pact?
She is a politician, so she is simply denying that GCHQ would ever do such things even though it has done them in the past. She is reiterating the previous claim that GCHQ doesn't circumvent laws and she is doing that for obvious political reasons.
Against the previous accusation of GCHQ circumventing the laws, Hague, then Foreign Secretary, said:
Hague added that it was "fanciful" and "nonsense" to suggest that GCHQ would work with an agency in another country to circumvent the law.
Even if they could admit any wrongdoing, hence technically breaking or circumventing the law, they would never use such a frightening statement. It's just something too strong to say for a politician, especially if it's true.
This is examplified by the statements of the then business Secretary:
"Well, it may well have been," he said, when asked if the allegations amounted to eavesdropping by any other name, and added that there were two key issues that the Tories would need to address.
In short, she wouldn't admit to be guilty even if she were. Why would she?
In any case, it wouldn't be illegal for the GCHQ to spy on an important candidate for President of the USA. Actually, it might be one of the few cases in which it would make sense to spy on someone. Since there would be a realistic chance of him being President and it might be important for the UK to know his positions on many issues.
Of course, the USA government wouldn't order the GCHQ to spy on an American candidate to the Presidency. But it wouldn't be that strange if the USA government asked if the GCHQ had some information on an hostile candidate and somebody would turn it over to a friendly candidate. A favor between friends, if you will. Especially useful, and likely to happen, if one candidate was sure to win and another was hated by both parties.
So, it might have happened, but we have no evidence for it. And if we actually found evidence of it most people would actually dismiss as the typical collaboration between friendly allies. Although somebody at the NSA and GHCQ might lose their job to save the face for the rest.