I have a slightly different theory to explain this conundrum. I don't think 了 directly acts as a "realis" particle to assert that something is factual; however, I think it tends to add such precision to the comment portion of a sentence that its use can help differentiate when a statement refers to reality or not.
In English, if I say: "I want to talk about your cousin getting a good job." You don't know the time frame of the job and whether the job is a past fact or maybe even just a hope for the future. However, if I say: "I want to talk about your cousin getting such a good job right after graduation last year after working so hard," you know I am referring to a past fact. If I say, "I want to talk about your cousin getting a good job as quickly as possible because the cousin has such potential and needs the money," you know I am referring to a future hope. By the rules of English, neither sentence actually makes any assertion about the factualness of the job, since a finite verb is not used to describe it. The two sentences simply refer to the status of the job with enough detail for you to work out whether or not the job is a fact or not. This is how I think Mandarin works and what 了 and other particles help to do.
When you say 她上个月去了北京, you are describing her trip to Beijing while specifically directing your listener to envision her as having completed the journey. This can sound incomplete if you do not immediately communicate why such precision about the stage of her trip is necessary in the discourse situation. If you follow up with a report on another event that took place after her arrival, probably while she was in Beijing itself, it will be clearer why you choose to be so specific and the sentence will be fine. Without an appropriate follow-up, it's as if the sentence only conveys: "I want to inform you about the aftermath of her arrival in Beijing." This is just a teaser that you want to say something else anchored in this time frame, but is not a good way to report on her trip as a whole. It sounds like an incomplete communication.
If all you want to do is report on the fact of her trip, you can just say 她上个月去北京了. This updates the listener about the trip without having to focus on her particular presence anywhere during the trip, which is not relevant to what you want to convey. You are just saying, last month she had a Beijing trip. Without 上个月, the timing of the trip becomes vague. Without 了, you are not updating the listener about the status of the situation, but naming some action, plan, habit, or idea relevant to the speech situation. Without any other words, it would be probably like saying: "I want to let you know about her Beijing trip(s)."
If you say 上个月我去台湾了, you do not tell your listener where to envision your location in the action, nor do you need to. You simply update your listener about your trip to Taiwan last month. Since this comment sounds like you are reporting a fact, it does assert a fact, even though there is no actual assertion morpheme in the sentence. I don't think you even actually assert that you reached Taiwan with this form of the sentence, although that would be have to be the assumption from such a simple sentence with no other very specific context. How can you inform someone of a trip to Taiwan last month without it having taking place, unless you go on immediately to do something like explain why it was only a tentative a plan that fell through or something similar?