It may well be that they don't want to cut their July vacation short by a day because they caught a cold in January. And to compound the issue, it was probably a cold they caught at work, because the company leave policy reinforces the behavior. People who stay home when sick are punished with shorter vacations.
I would not want to be in a situation where my vacation time depended on some prevailing sense among coworkers of the appropriate number of days to take off.
It's been the case at the last four places I worked: large corporations who knew their H1B workforce wouldn't ask for time off, and startups where I wouldn't get any spare moments to meet with my managers to ask for vacation.
(Fwiw, the vacation time at the start ups was perfectly decent, given the situation. I think I took ~3 weeks off each year. At the big company, it was a total fiddle.)
In this particular case though, possibly just how lucky I am to live in Australia. Here it's either just common practice at most companies, or possibly required by law, but everywhere I've seen the leave policies provides 52 weeks a year of sick/carers leave.
Usually this is broken up into ~20 days of leave where one isn't really required to provide any justification beyond "I felt bad that day" and beyond that a doctors certificate may be required.
But that's always entirely separate to annual leave.
I read this and go '52 weeks a year for sick leave? Aren't there 52 weeks in a year total?'
Very, very tiny consolation. I'd live with a dog-sized spider if it would mean that corporate management wasn't filled with cold-blooded monsters.
Some uptight employers require a doctor's note but most just roll with it.
That always stuck me as a profoundly civilized attitude.