150 kg being too heavy to lift for an ambulance EC-135 is not very believable.
Screenshot above is from this site, stating a max payload/fuel weight of 1,375 kg with one 80 kg pilot on board. With a maximum fuel load of 560.4 kg, this leaves 814.6 kg payload capacity.
The advanced rescue EMS kit is depicted on page 56, including 2 seats, a stretcher, life support & oxygen systems etc, and is stated to weigh 142.1 kg. With 2 medivac personnel plus a co-pilot of 80 kg each and maximum fuel on board, patient weight capacity would be 432.5 kg - a lot more than the 150 kg that supposedly Bild claimed was too heavy for the helicopter. (Tried to verify on Bild.de but did not want to agree to advertising cookies).
The EC-135 is a twin engine helicopter that can continue flying and landing upon a single engine failure - even taking off with One Engine Inoperative is possible with a reduced gross weight of 2,870 kg @ ISA + 20°C. So even with OEI, a patient of 150kg would be no issue.
Another possible problem could have been the physical size of the patient. The payload section of the cabin interior measures 2.5m long and 1.5m wide. It is possible to place 3 seats side-by-side - at 50 cm each that would leave about 1 metre width for the patient. Loading a stretcher with 150 kg on board could be an issue with handling - but there are systems designed for handling patients over 300 kg (bariatric patients), as mentioned on this site:
“On the rotor wing operation, Ornge has invested in ensuring we have the right aircraft with the right equipment to maximize support for bariatric patients,” said Pyke. “Our AW139 helicopters are well equipped to handle bariatric patient operations. We have partnered with HeliMods to install a PAL system based on Stryker power equipment. This provides a no-lift solution to loading and securing of patients up to 700lb (318kg), depending on clinical equipment requirements.”
The linked RTL article states in the headline that the patient was too heavy, in the article itself mentions (translated from German):
According to the fire brigade, however, the helicopter flies back without the man, as the 30-year-old does not fit into the helicopter due to his weight and size.
So there was a size and weight issue - indeed perhaps a stretcher issue as @GremlinWranger suggests in a comment, however not a payload issue.