The phrase "alternative facts" is not really new.

It is a US law practice phrase.

For example:

From Family Law in Practice:

Provided the alternative facts or the alternative interpretation you put is reasonable, an expert who resists such a suggestion looks less credible.

From Guide to Computer Forensics and Investigations (2014):

You might want to address alternative facts, however, if they allow your opinion to remain the same. The expression “alternative facts” might seem contradictory, but it simply means competing facts.

From The Art of Lawyering (2010):

The proof will be in the experts' ability and willingness to handle alternative facts in their own theories or to apply alternative methods than the ones upon which they rely.

And even over 100 years ago The Lawyers Reports Annotated, Volume 51

There is no effort in this pleading to allege alternative facts.

So alterative facting should mean providing actual true facts, that emphasize a different desired conclusion.

However, "alt-facting" is new and alludes to Alt-right.

The phrase "alternative facts" is not really new.

It is a US law practice phrase.

For example:

From Family Law in Practice:

Provided the alternative facts or the alternative interpretation you put is reasonable, an expert who resists such a suggestion looks less credible.

From Guide to Computer Forensics and Investigations (2014):

You might want to address alternative facts, however, if they allow your opinion to remain the same. The expression “alternative facts” might seem contradictory, but it simply means competing facts. In a civil case, if there weren't alternative possible facts, the case wouldn't be at trial; it would have been decided at summary judgment.

From The Art of Lawyering (2010):

The proof will be in the experts' ability and willingness to handle alternative facts in their own theories or to apply alternative methods than the ones upon which they rely.

And even over 100 years ago The Lawyers Reports Annotated, Volume 51

There is no effort in this pleading to allege alternative facts.

So alterative facting should mean providing a competing theory of what the events actually were, based upon true evidence.

However, "alt-facting" is new and alludes to Alt-right.