First of all, if your place has things broken willy nilly, you are putting the carriage in front of the horse! You need an entire IT strategy that works, because the one you (they?) are using doesn't. While there needs to be a sense of priorities, if there is that much in need of doing that a tech cannot take care of something else while he/she is already there, it is a symptom of a broken system.

"...if you did, your boss might smack your wrist very hard..."

Yeah, I totally get this. The person that tries the hardest is usually the one in the most trouble, while the slackers never get noticed or reprimanded. That isn't just IT, that is life in general. (And God Forbid someone actually gets something accomplished...)

Back to the subject:

I am frequently flagged down or waved over while walking through the offices. I would NEVER give someone a rubber stamped reply like "...fill out a ticket..." Sometimes they are asking me for something that is beyond my limited authority to do, and then I will politely explain that and tell them to send an email to my boss about the problem, and it will trickle back to me with instructions how it is to be handled. Otherwise, if it is a software or hardware issue, I most certainly will fix it right away, or arrange to get back to that person. (I might ask them to send me an email as a reminder. I am forgetful like that, and my co-workers appreciate the honesty as much as I appreciate the reminder.)

I am not the primary IT person here, but I am the primary Help Desk person, and I try very hard to make my customers, (my co-workers) satisfied. Our dept. gets calls and emails. We do not use a ticket system. I suppose that if we were larger, it might become a necessary evil, but right now, email for non-urgent jobs, and phone calls for urgent matters. If I am away from my desk, I get the voice mail message and get back to them as soon as I am able.