Deductions & credits

According to tie-breaker rules posted at <a rel="nofollow" target="_blank" href="https://www.thebalance.com/claiming-dependents-3193028">https://www.thebalance.com/claiming-dependen...>,
the parent has first option to declare the child as a dependent.  It doesn't say anything about actually supporting the child or living with him.  Is that correct information?
The rules show are:
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The taxpayer most eligible to claim a child as a dependent under the qualifying child criteria is:

    A parent
    The parent with whom the child lived for the longest time during the year. Chances are the child will spend at least one day more with one parent than the other parent because there are usually 365 days in a year.
    The parent with the highest adjusted gross income if the child spent exactly an equal amount of time with each of them.
    If neither taxpayer is the child's parent, the taxpayer with the highest adjusted gross income gets to claim the child.