The phrases in the quotes: (the winter solstice according to the astronomical calculations of that time) and the inaccuracy of the calendar indicate to me that according to the astronomical calculations of our time, and the accuracy of our calendar, they were wrong. Perhaps you understand those phrases differently.
I trimmed your quote down to just the discussion you had with me, I have not addressed the reason for December 25 so I'll not address those and leave it to others to argue.
I only pointed out that you said the articles stated that the Romans got the the solstice wrong, but the Romans DID know when the solar solstice was. The
astronomical calculations of the solar calender of our time are not different than their time, the name of the date on the proverbial wall calender changed. We have changed the wall calender, the wall calender we use is more correct than theirs was. When we changed the calender, Christmas stayed with Dec. 25, but the solar calender of the astronomical calculations refused to recognize the authority of Gregory to change the calender and stubbornly kept the winter solstice right where it had always been, so now the winter solstice falls on what we call Dec 21st or Dec. 22nd, depending on which year it is.
The Romans could very well determine, accurately, when the solar calender's winter solstice occurred, and your articles said the same thing I said.