He would say that, wouldn't he?
I start from the assumption that Fleming and his staff basically are decent people. That applies also to MI5, MI6, and the plethora of other security/police agencies operating within or beyond the public gaze. Many such people are competent too.
That said, I don't trust GCHQ or any other UK-linked security/surveillance agency one jot more than absolutely necessary i.e. very little at all. It's no so much existence of these agencies that offends me but rather the creatures within whose purview the agencies fall i.e. their political masters. Politics never has greatly attracted people of intellect, broad education, taste, wisdom, and unbending probity. The quality of personnel in the British legislature's two chambers declined markedly when Blair took office and continues at a level of incompetence and peculation more fitting to the eighteenth and early nineteenth centuries. Observe how these non-entities assiduously proclaim their importance, dignity, and entitlements despite the fact of few possessing merit and those holding executive government posts barely capable of running a whelk stall in Brighton. Watch them in their chambers, particularly the lower one, mired in anachronistic customs and practices, and stuck with speeches, so-called oratory, as means of communication within their Houses.
That's not to say there weren't in recent times figures of stature. Churchill, Bevan, MacMillan, Wilson, Powell, and Wedgwood-Benn come immediately to mind. Doubtless some genuine talent coupled with personal integrity persists, though unlikely to be found in the Cabinet.
At one time, people appointed to senior ministerial positions usually had sharp enquiring minds. Ministers, in general, were not placed in charge of departments on the basis of subject matter knowledge and skills; indeed to do so risks blinkered vision and attitudes. It was, perhaps still is, if anyone bothers to think on it, customary to put generalists rather than specialists in charge. Thus, a minister is expected to quickly come up to speed on policy issues. He is not required to master fine detail and associated technologies. Yet, when allocating budgets and preparing legislation he must be fully aware of the consequences of his choices. Only a fool would rely upon receiving accurate and unbiased advice from civil servants and brought-in expertise. Underlings likely are reliable and honest but a minister should give as much due diligence to disbursing public funds as he would when buying a house for himself. Thus, a sharp interrogative mind is required. One able to ask penetrating questions and recognise bullshit when proffered it. By making pertinent enquiry a mind trained in any rigorous discipline is capable of fathoming the most complicated of matters sufficiently to make informed decisions.
Present day reality departs widely from the ideal. Would-be career politicians are a curse on society. They do the 'right things' such as the almost worthless Oxford PPE (designed to enable dim sons of monied gentlefolk to make contacts in Oxford's social milieu). They proceed to suitable 'stepping stone' employment (if on the 'Right' something in the City, if on the 'Left' office in a trade union, deadbeat lawyers abound too).
Imagine the likes of these interacting with Jeremy Fleming or the heads of other agencies. With reference to GCHQ there is high likelihood of its overmaster politician at any point in time being a proud mathematical illiterate (read English literature and nothing more) and incapable of grasping the concept of encryption/obfuscation beyond simple letter substitution. Fleming, and colleagues elsewhere, doubtless put forth plans and schemes with sincere intent; regardless of that, there cannot be proper governance unless the minister is capable of formulating penetrating questions.
The UK is, in effect, ruled on all matters truly important to the 'establishment' by an inner cabal of the Privy Council. This arrogates responsibility for foreign relations, defence, and security. It serves the wishes of its true 'deep state' masters (e.g. political party donors, conglomerate tax avoiders, financiers, and defence equipment manufacturers) using instruments known as royal prerogatives left over from the Act of Settlement. So the position is of ministerial monkeys representing de facto departmental organ grinders on the one body in the land with sufficient power to cock matters up royally.
GCHQ and similar can earn trust in two ways. First people from government being indisputably capable of policy direction and prudent budget allocation to the agency. Second, considerably lifting unnecessary shrouds of secrecy to enable informed opinion to judge whether agencies deliver that requested of them in cost-effective manner, and don't depart from their remit.