In media interviews be especially careful.
Use 'sorry' or 'apology' the wrong way and it could cost you, in public perception or in court, or both.
Many interviewers don't understand the difference themselves.
The airline Jetstar once grounded its planes, because of volcanic dust from a Chilean volcano... a safety measure, of course. Mary Wilson, a high profile radio interviewer grilled a Jetstar manager (with a hostile, accusing tone) as to why the airline had not apologised to their grounded passengers for the inconvenience.
An apology? Oh no. Don't fall for that.
An apology is for when you (or your company) have done something wrong - made a mistake, acted in bad faith, acted recklessly or with poor judgement. In other words when it's your fault.
Sorry is for when you feel badly about someone's distress (which may or may not be connected with any action of yours).
Sorry is not an apology, it's human, 'no-fault' empathy. So when you're faultless, don't say 'We apologize.' For the Jetstar manager it would have been safer to say, 'Apologise? No, of course not, we haven't done anything wrong. But we are sorry that our passengers have had to put up with all the frustration and inconvenience.'
So is it safe to say 'we're sorry' in a media interview?
The words 'sorry' and 'apology' are so thoroughly confused in the public mind that either can bring you trouble. For example: suppose you're the manager of Black Velcro Coaches; and recently a passenger, Helen Smith, broke her ankle when the bus braked sharply. You felt for her pain (being a real human being) and said in public, 'We're sorry this happened.' Now, in court, the complainant's solicitor says, 'Your honour, the company has apologised, thus admitting liability.'
So if liability could be an issue, it's much safer to avoid both words. Which leaves this question. If you have normal human empathy for the distress of others, how do you express it safely?
How to show empathy without saying something risky
Here's how. Keep yourself (I, we, the company) out of the statement and talk only about the injured party and their feelings. Typically, 'It must have been upsetting and painful for Helen Smith.' No legal ripples.
One more thing, you can't afford to be paranoid about the confusion. If you are found liable for someone else's distress and (out of wariness) never expressed empathy, that can be very expensive indeed. Complainants' solicitors can then say, 'Your honour, at no stage did Black Velcro Coaches express any kind of sympathy for my client. We're asking for exemplary damages.'