Last time I checked, the United States of America was a democratic country.
Last time I checked, the United States of America is a democratic country.
Any preference or right/wrong above?
To this US English speaker, of the two choices given above, only the past tense sounds correct. Whether the fact is still true or not, we are talking about what was true at the time the speaker last checked, which must be in the past.
Consider an alternative example which might make it clearer:
The last time I visited Spain, the beaches are/were closed.
Which one sounds correct? Clearly only were closed, because we are talking about what was true then, not what is true now. The beaches might or might not be closed now, but that is not what we are talking about.