My question is not about the Phantom Time Hypothesis, but maybe Phantom Time on smaller scale with few years more or less as a mistake?
I was recently reading about how the calendars developed and at moments it seemed very easy for those scholars to make mistakes.
For example how even Anno Domini was calculated isn't very convincing:
It is not known how Dionysius established the year of Jesus's birth. Two major theories are that Dionysius based his calculation on the Gospel of Luke, which states that Jesus was "about thirty years old" shortly after "the fifteenth year of the reign of Tiberius Caesar", and hence subtracted thirty years from that date, or that Dionysius counted back 532 years (the period during which the dates of Alexandrian Easter repeat) from the first year of his new table.[18]
It has also been speculated by Georges Declercq[19] that Dionysius' desire to replace Diocletian years with a calendar based on the incarnation of Christ was intended to prevent people from believing the imminent end of the world. At the time, it was believed by some that the Resurrection and end of the world would occur 500 years after the birth of Jesus. The old Anno Mundi calendar theoretically commenced with thecreation of the world based on information in the Old Testament. It was believed that, based on the Anno Mundicalendar, Jesus was born in the year 5500 (or 5500 years after the world was created) with the year 6000 of the Anno Mundi calendar marking the end of the world.[20][21] Anno Mundi 6000 (approximately AD 500) was thus equated with the resurrection and the end of the world[22] but this date had already passed in the time of Dionysius.
Yes, absolutely, due to astronomy. Several rare astronomical events have been recorded in ancient history. Things such as eclipses, occultations, conjunctions, etc. We can determine the exact relative timing of some of those events due to the deterministic nature of astronomy, and so pin down different calendars in different eras relative to each other down to a precision of at least one day.
Meaning that there are no missing days between today and several hundred years bc, and for many sources we can conclusively say exactly how many days ago certain dates were.
As to whether or not the whole ad/bc scheme is fixed to the actual birth date of the historical individual who is the basis of the religious stories about Jesus, that's still an open question and may well remain one forever.
As /u/rocketsocks says, we can pin our own position in time relative to other described positions in time with relative certainty, due to our ability to calculate astronomical phenomena.
The other part of your question though - is it "really" 2016... yes. Why? Because we said so. The idea of a date is completely arbitrary and human-created, so it "really" is whatever year everybody gets together and says it is. It's really 2016 - it's also really 4713 (Chinese calendar), really 5776 (Hebrew calendar), really 1437 (Islamic calendar), and really several other years as well, depending on the tradition in use.
Bede's Ecclesiastical History of the English People is a fascinating read for many reasons, but one that I like in particular is seeing the different ways he records years. He makes a point of writing the year in multiple systems, and over the course of the book (which took multiple years to write) one can see the slow shift occurring from an older system to a newer system, with which he prefers shifting over time.
There's always room for discussion, but perhaps the section Calendars and Timekeeping in our FAQ located in the sidebar will answer your inquiry.
There isn't even evidence of Jesus to begin with...