No.It was never claimed. A feast day was needed. December 25 was the choice the Romans made for whatever reason, perhaps to preempt Saturnalia, perhaps because that day was open on the calendar. We are not privy to the minutes of the meeting.
You are incorrect. There are MANY claims of the ancient Church that support the December 25th date.
The idea of the Christians “stealing” Dec. 25th from pagans is overblown in my opinion.
A Roman civil calendar of 354 has the 25th as the birth of the “unconquered”, i.e. Sol Invictus. An ecclesiastical calendar of the same date shows the 25th as Christ’s birth. The Roman cult of Sol Invictus is not an early one—it is Mithraic, which dates to the 1st century *at the earliest*, so it is no older than—and probably actually later than Christianity. In any case, saying that one stole from the other is largely speculation—they both appear at the same time.
Here’s the civil (i.e. pagan) calendar of 354. Hope you brushed up your Latin! :)
http://www.tertullian.org/fathers/chronography_of_354_06_calendar.htm
There is other evidence that needs to be taken into account. Chrysostom said that the Romans celebrated Dec. 25th as Christmas “anothen” = “from the beginning.” and said that they calculated the date from the census records in Rome. Clement of Alexandria said that in his day (200s), people believed Christ was born on 25 Pachon or 25 Pharmuthi. Those are Egyptian months and would put the Nativity around April/May; but the “25” date is interesting.
Anyway, the various calendars in use back then and the possible ways of translating a date make it especially frustrating. Say Christ was born on 25 Kislev on the Hebrew calendar (i.e. Hannukkah). 25 Kislev was Jan. 6th in 4 B.C.—perhaps that’s how the date got attached in the East. Kislev is the 9th month, so perhaps some in Egypt made it the 25th of their 9th month (25 Pachon). And perhaps the Romans took the 25 date and considered the time of year and made it Dec. 25 (their 9th month being November).
There aren’t any pat answers for this. Neither did the early Church—which explains why a range of dates was suggested. And they’d know better than we would.