Saluting / Greeting with Arms Encumbered

So I'll set the stage by giving you the scenario and you can tell me if you think I was wrong or if the MSgt was wrong.

I met my wife in the parking lot outside my building to walk with her and my two year old back up to my office to eat lunch. I was walking across the parking lot while holding my son's hand with my right hand and hold my lunch in the other hand (arms obviously encumbered). As I'm walking to the building, a MSgt from another section walks out. I know her because she works in the same building with me and that's about it - no interaction at work at all. She looks at me and I am talking to my wife and helping my son step onto the curb. She extends no greeting to me and continues to walk past me to her car. I didn't really think much of it and I'm not going to call her out for not greeting/saluting me with my wife and kid walking with me into the building. (plus, I wouldn't normally do it anyway unless I'm sure it was intentional)

The next day, another Major in my office (her boss) comes to talk to me and tells me that the MSgt “has a problem with me” and was complaining to him that I “actively avoided” her yesterday in the parking lot and did not offer her a proper greeting or salute. I was taken aback that she would bring it up to her boss. Last time I checked an O-4 outranks an E-7 and I don’t owe you a salute or greeting – it’s the other way around. I thought I was being nice by letting her off the hook the day before and then she tries to turn it around on me and call me out to one of my peers in the office. Unless I’m absolutely failing at my reading comprehension below on these excerpts from AFI 34-1201 and AFPAM 34-1202, it is the MSgt’s responsibility to render the salute and verbal greeting and my responsibility to return both (or at least the greeting if my arms are encumbered). [end rant]

I basically told the other Major that I didn’t really care what she thinks. I was not “avoiding her” and obviously saw the situation the other way around. I told him that the next time it happens I’ll be sure to drop my lunch and let my 2 year old run off into the parking lot so I can render the proper salute and greeting to this obviously entitled MSgt.

AFI 34-1201:
8.1. Hand Salutes.
8.1.1. The hand salute is the form of greeting and recognition exchanged between persons in the armed services. All Air Force personnel in uniform are required to salute when they encounter any person or situation entitled to the salute.
8.1.1.1. When the salute is rendered to another person, the junior member initiates the salute accompanied with an appropriate verbal greeting, e.g., ―Good Morning, Sir/Ma‗am.‖ The salute and a verbal greeting should be extended at a distance at which recognition is easy and audible. The salute should be offered early enough to allow the senior time to return it and extend a verbal greeting before passing. All salutes received when in uniform shall be returned; at other times, salutes received shall be appropriately acknowledged.

AFPAM34-1202
8.4.6. Exceptions to Saluting.
8.4.6.1. Rendering a salute is not required when arms are encumbered. However, one should always extend a verbal greeting or respond to one in such a circumstance. (Note: You should always salute a senior officer if he/she is encumbered and you are not, even though the salute cannot be returned.)