I was told that earlier wounds would increase the chance for fungus to get in?
It is always a possibility. Many of us pucker over pruning during winter because it exposes cambium and xylem while the tissues are snoozing, which means the normal CODIT reactions are s l o w. The counter argument is that pathogens are also s l o w to act when it is cold.
I'm familiar with two particular pathogens of this ilk in Japanese maples, verticillium and nectria.
Verticillium is soil borne, and could get into the exposed xylem if one grabbed a handful of bad dirt and rubbed it on OR if the girdle was near ground level and left open in the rain (verticillium being splashed up onto the girdle). I layer landscape trees and do leave girdles open for at least a day to kill residual xylem initials (to prevent bridging), but never during a rain event. Alternatively, I wipe down girdles with a paper towel dampened with 70% isopropyl alcohol, just as I do all my cutting tools before use. I will further note that verticillium is nixed by a year of thorough, natural composting (be wary of new landscape soil)
Nectria invades both phloem and xylem, so it too could get into a girdle. But nectria fruits in mid to late summer. Few spores are around at any other time, so it isn't a worry with girdles made in the spring. However, I did once have a new landscape tree affected by it, but didn't realize it until later when I had already spread it to two other of my landscape trees by my tree saw and pruners. As a consequence, I always sanitize my cutting tools, including my grafting knife by wiping them with an alcohol soaked paper towel (sanitary wipes will work as well). I have seen the orange fruiting bodies of nectria on several occasions on nursery stock. It becomes a problem because the sales people think it is an innocuous 'orange stuff' that they just prune off the inventory as it show up. If you've never seen such 'orange stuff' on branches that suddenly went brown, you probably don't need to worry about it.
So, bottom line, I don't think this is serous concern, generally speaking.