adverbs - Does "regardless" require an object?

I was once told that it's incorrect to begin a sentence, "regardless, . . . ." Instead, one must specify "regardless of" something.

E.g., "Regardless, they should not have skipped out on the check" should be "Regardless of the bad service, they should not have skipped out on the check."

Does it matter whether the preceding sentences explain the "regardless" issue? E.g., if there are three sentences explaining why the service was bad, it is then ok to write "Regardless, they should not have skipped out on the check", the assumption being that it's clear in context what the "regardless" is addressing?