In light of the bad publlicity faced by Pirelli, not just these past few days but over the course of the season, it would be easy for it to bow out this season with the expiry of its three-year contract.
Sunday's British Grand Prix, during which there were a number of high-speed blowouts that endangered the lives of not just the drivers, but also marshals and fans, was Pirelli's nadir.
Even Hembery claimed it was the first time anything like it had "ever occurred in more than a century of Pirelli in motorsport".
Hembery, however, has insisted Pirelli has responsibilities it takes seriously and is determined to right the wrongs.
Asked by Press Association Sport whether the company wants to continue in F1, Hembery replied: "Yeah, you have to.
"We need to get it sorted and the best way to react is do it properly and get things back on line.
"We are a professional company. We are very passionate about what we do and very good at what we do.
"You don't walk away in difficult times. That's the time to work harder and make sure you do a better job."
As for beyond this season with a new contract, Hembery added: "Yeah, sure."
Pirelli, though, is under enormous pressure at this weekend's German Grand Prix to prove its tyres are safe.
Only yesterday the Grand Prix Drivers' Association (GPDA) threatened to not run should there be a repeat of the incidents seen at Silverstone.
That followed a meeting between the GPDA and Pirelli race director Mario Isola, to which Hembery said: "It (the statement) was a little bit surprising given the meeting we had with them to go through it.
"At the end of the day we have to make sure we don't have any issues like we had at Silverstone. That's the bottom line.
"So we tried to explain the situation, what's happened, where we've been this season, the different evolutions.
"Maybe it's not always clear to them what goes on. There's a lot of dynamic involved in the sport, different teams, different interests.
"We also explained the changes here and the changes going forward, which we believe are in completely the right direction for them."
Earlier this week, following what Pirelli described as "exhaustive analysis", it highlighted a number of factors behind the blowouts.
They included the practice of the teams swapping the rear tyres, too-high pressures and excessive cambers.
Ahead of Friday's practice sessions at the Nurburging the FIA issued a note to all the teams, following a request from Pirelli, detailing the correct tyre pressures and cambers, and stating the front and rear tyres must be used on the correct side.
Hembery added: "We wrote to Charlie (Whiting, race director) and asked him to write to the teams defining what we require.
"That was because despite what happened last weekend we've still had some people asking to do things we didn't want them to do.
"I have to say last weekend was our responsibility. We allowed the teams to invert the tyres when we shouldn't have done.
"With the cars going much quicker this year that creates different loads. With the inverted tyres you create a weakness point, and that was the issue.
"There were secondary issues, which have been mentioned, but I don't want to take away from the fact it was our responsibility.
"Going forward, though, there are things we need to be much more rigid on and that's where we are at."
For this weekend the cars are running on Kevlar-belted rears as opposed to steel, while from the race in Hungary later this month the tyres will comprise last year's structure with this year's compounds.