Interpretation is the key.Not logical my friend. The two statements are stand alone. One does not contridict the other.
Now here is an example of an alternative fact using your comment:
1 "I saved 20% last night on my shopping trip to Bed Bath and Beyond."
Alternative facts:
1. "I saved 75% last night on my shopping trip to Bed Bath and Beyond."
2. "I saved nothing last night on my shopping trip to Bed Bath and Beyond."
annsni's interpretation of alternative facts is correct.
OTH so is your alternative interpretation of alternative facts.
Differing alternative facts can indeed appear paradoxical.
HankD