One of the main factors in determining a company's credit rating and therefore its cost of debt is a ratio called 'interest coverage'. This is earnings (EBIT) divided by interest expense. So, the higher the level of debt, the higher the interest expense, the lower the interest coverage, the lower the rating, therefore the higher the cost of debt. While UPS may have enjoyed favorable rates at the time of the debt issuance, there is no guarantee those favorable rates will exist when the debt needs to be refinanced. In fact UPS' debt was downgraded following the debt issuance. Keep in mind at the time UPS offered the notes creating the current debt levels, the economy was fairly normal--January 2008. Times have changed, quite obviously. The cash-generation abilities of most companies aren't what they used to be, UPS included. As the fineprint in the investor-oriented ads always warns 'past performance does not guarantee future results.'
The need to refinance the capital structure at less favorable rates is a risk worth noting. In addition to the refinancing risk, there is the risk (albeit low, in this case) of default. You see, bankruptcy is triggered by one thing and one thing only--the inability to pay creditors. The more you owe, the higher the risk of bankruptcy. Owe no one, and no chance of bankruptcy. Of course, there is always someone to pay, even without long-term debt--current accounts payable, for example. But simply put a more-levered UPS is more at risk.
As far as the company's choice of debt financing vs. equity financing--there is a prominent view (from Modigliani & Miller) that capital structure is irrelevant. Because debtholders are ahead of equityholders in terms of being paid, the cost of debt (based on risk) is always lower than cost of equity (equity holders require greater return to offset more risk). Therefore, a higher proportion of low-cost debt in the capital structure does not lower a company's total cost of financing since the presence of that debt creates an increase in the cost of equity.
BTW--I believe this is the BusinessWeek article to which you are referring:
http://www.businessweek.com/magazine/content/01_21/b3733084.htm
It's from May 2001- a bit outdated, so I would not assume it reflects current conditions, but yes, an interesting read nonetheless.