When I think of someone writing about office hours, or an hour at the office, I think of the words “office hours”, because in this case they are not being used as separate words put together (office + hours), but as one phrase that means a time spent at the office. I think your friend is thinking of the words as separate, their meanings individually. But put together and the plural “hours” doesn’t necessarily mean it has to be used for multiple hours.
For example, do you mean something like this?:
During my office hours, I spent an entire 45 minutes trying to print a report just to find out that my computer had somehow disconnected itself from the office network.
There are several variants of this, "24/7", "24-7", "24/365", "24X365" and so on.
Those with a multiplication are clearly depending on the fact that e.g. 24×7 will indeed, if calculated, give the number of hours in a week.
The main point of that expression is not to convey 168 nor for "24×365" to convey 8760 (which forgets leap years anyway). It's to convey that information which is also available in the forms which don't use the multiplication symbol, viz that the service, shop, etc. is available at every hour and at every day of the week and/or year.
"24-7-365" conveys availability at every hour and at every day of the week and at every day of the year. The "7" is redundant when we have the "365" but it relates to a different concern: It might be more important to me that a service is available on Saturdays than that it is available on Christmas, so I might care about the "7" more than I do about the "365" even though the latter logically entails the former.
The mathematically incorrect "24×7×365" is just a merging of that with the forms where the arithmetic actually does work, because similar common expressions will always end up being merged, especially when written quickly.
Best Answer
Both of these are equally good with hours and other common measurements. But maybe not with less common measurements. For example:
is more common than