During his playing years as English football’s most famous striker in the 1980s and early 1990s, Gary Lineker was never cautioned by a referee or sent off the pitch. It was not until after his playing career that the referees at the BBC blew the whistle.

As the world now knows, the star football pundit, host of the BBC’s flagship Match of the Day programme and its highest paid personality, was benched last week over fears that his tweet about the Government’s new immigration Bill compromised the broadcaster’s commitment to impartiality. The sound that followed was the deafening roar from the footballing world flooding the pitch to back Lineker.

After a weekend of curtailed programming and resignation threats from other top hosts, the BBC announced yesterday that, lo and behold, it will bring Lineker back on air. The Beeb apologised for “potential confusion caused by the grey areas” of its social-media guidelines and will subject them to an independent review.

So Lineker will return to his chair, along with his famous co-commentators, Ian Wright and Alan Shearer — both had walked out in solidarity with Lineker — ahead of the weekend’s crucial matches. That comes as a great relief to Lineker’s, and football’s, many millions of fans. But it leaves a big question mark over the BBC’s governance. Instead of defending impartiality, as it must, the BBC reaction exposed its own guidelines as fuzzy and their application as random.

The existing guideline notes that individuals identified with the corporation “have the potential to compromise the BBC’s impartiality and to damage its reputation”. But the next paragraph says that “the risk is lower where an individual is expressing views publicly on an unrelated area, for example, a sports or science presenter expressing views on politics or the arts”.

Lineker has always maintained his right to talk about issues he cares about. While broadcasting from the World Cup, he was not shy to call out Qatar’s human rights record. If that made the BBC uncomfortable, it did not lift a finger to stop him.

There is no reason that sports or entertainment personalities should not have some room to express their views on issues that matter to them on their social-media channels, even when that is inconvenient to the government of the day. Indeed, other major personalities from Brian Cox to David Attenborough have done so. Most people are able to differentiate between a sports pundit who expresses a view on an issue and a political presenter who does so. Clearly, there are boundaries, but the BBC should err on the side of free speech.

The longer-term damage to the BBC here is not from one bad call, but the appearance of a double standard when it comes to integrity.

The selection of BBC chairman Richard Sharp — a generous donor to the Conservative Party in the past — is the subject of an investigation after it emerged that he had facilitated an £800,000 (about $966,720) credit facility to his friend, Boris Johnson who was then prime minister, at a time when Sharp was a candidate for the BBC job. Sharp made clear since that he had made an introduction to a government official who could advise on the matter and was not himself involved in making or arranging the loan. (A parliamentary committee report concluded that Sharp had made “significant errors of judgment” and called on him to “consider the impact his omissions will have on trust in him, the BBC and the public appointments process”.)

Still, it struck many as suspect that a broadcaster whose leadership has numerous Conservative Party ties cracked down on a sports pundit who was criticising a Conservative Government policy. The irony is that Johnson spent much of his time in office criticising the BBC for bias in the other direction. The BBC’s job now is not just to straighten out where its impartiality guidelines apply to presenters, but to ensure that its own leadership is viewed as unimpeachable.

The whole saga is awkward for the Government, too, despite the free advertising its immigration Bill has received. It is nearly always counterproductive and wrong to invoke Nazi Germany to make a political point, as Lineker did in his tweet. Lineker’s broader point, however, was to note the dangerous rhetoric underpinning a Bill that essentially makes it illegal to claim asylum in Britain and which, by the Government’s own admission, is very likely a breach of international law. By noting the “immeasurable cruelty” of the Bill, Lineker was making a moral argument that even the Labour Party, equally keen to be seen as tough on migrants, has shied away from.

Nor is Lineker about to give up talking about the issue. “However difficult the last few days have been, it simply doesn’t compare to having to flee your home from persecution or war to seek refuge in a land far away,” he tweeted yesterday. “It’s heart-warming to have seen the empathy towards their plight from so many of you.”

In a few spare moves, then, Lineker has shown up the flaws in the BBC’s governance, the cynicism at the heart of the British Government’s immigration policy and the hollowness of the Labour Party’s carefully curated indignation — a hat-trick from a pundit who still has game.

• Therese Raphael is a columnist for Bloomberg Opinion covering healthcare and British politics. Previously, she was editorial page editor of The Wall Street Journal Europe