First off, what many people claim are spiders bites in fact aren’t spider bites at all. Could be centipede bites, mosquito bites, bacterial infection, rash, etc. Unless you see a spider actually bite you, there is no way to tell a spider bite by just looking at it. Spiders rarely bite people, as we are not food, spiders are rarely that aggressive, we are too large for them to comprehend, and should a spider bite you, which is very rare, the venom is much too weak to do anything except create a welt. 80% of Brown Recluse bites do NOT require medical treatment. The average person can NOT tell a Brown Recluse just by looking at it. Hell, even I can’t and I make it a point to study spiders. I’ve seen a lot of brown spiders in my life, but I am pretty sure none were the much feared BR. They just aren’t that common here in the North.
Second, spiders you find indoors have evolved to live indoors. Taking them outside is a sure death sentence. Outdoor spiders only get indoors by being on something we bring in from outside. Outdoor spiders have no reason to come indoors, not even in the fall.
Third, while the bug you saw on your desk might have looked like a bright red spider, more than likely it was a mite. There are types of mites you find on indoor plants that look like tiny spiders but in fact are not.
And lastly, Much lurve to dynamicduo for having the sense to realize that insects are the least of our worries. Bugs can’t hurt you, unless you live in the tropics or somewhere in the southern hemisphere where dangerous insects and spiders thrive.