The man, from Wakefield, had been given the diagnosis on a remote appointment with a consultant, it was revealed last month.
Local Labour councillor Charlie Keith described the incident as "unacceptable".
Now Coun Keith said the patient in question had received an apology from the health service.
But people with lung cancer are among those still receiving diagnoses over the phone, as opposed to face-to-face, it's been claimed.
Local NHS chiefs say doctors and staff are working "harder than ever before" and that they're offering face-to-face appointments to those who need them.
Speaking at a scrutiny committee on Thursday, Coun Keith, who represents the Wrenthorpe and Outwood West ward, said: "I mentioned at the last meeting how somebody learnt they had 12 months to live over the phone.
"It's not just GPs - this is clearly happening at consultant level as well.
"Since the publication of that in the press, there's been much rowing back on that. An apology has been made to that individual and it's been addressed.
"But since that story was picked up on in the press, many people have come to me and expressed similar concerns."
Coun Keith said many patients were not receiving the service "they've paid for up front" from the NHS.
Representatives from the local health service listened as councillors told multiple stories about residents struggling to access the care and attention they need.
Committee chair Betty Rhodes said the levels of care being offered at GP surgeries across the district was unbalanced.
She told the meeting she knew of one woman who was misdiagnosed with Parkinson's disease over the phone.
She added: "I know of a lady who had a call from her surgery to say she had lung cancer, over the phone.
"This is just a sample of what we're all hearing and it's time these people's voices were heard.
"We're not saying there aren't good practices, but we're saying what is on offer should be the same everywhere across the district.
"The situation is getting beyond belief now for some people.
"To have people at the other end of the phone being told they have lung cancer, I think there's something radically wrong with the system."
Lupset GP Dr Adam Sheppard told the meeting that a shortage of doctors was contributing to the problems.
It comes at a time when demand for all aspects of healthcare is now at record levels.
Dr Sheppard said: "I've been a GP for 30 years. From my own perspective I'm working harder than ever.
"In my day-to-day practice I'm dealing with more consultations than I did pre-pandemic."
Dr Sheppard said some patients preferred telephone appointments, as it meant they didn't have to take time off work to resolve an issue that did not need face-to-face contact.
But he said he accepted that "isn't right for everyone".
Mel Brown, from Wakefield Clinical Commissioning Group (CCG), which oversees local NHS surgeries, said: "I don't want anyone to go away thinking that staff aren't working hard.
"They've never been as busy as they are now. They've never worked so hard."
Local Democracy Reporting Service