I have not read that whole SEP page for now, but at first glance the paragraph you quoted seems quite questionable to me.
First of all, there is a big "if not, then" in there. It seems in no way clear to me that there is an implicit assertion that the answer is "yes". It seems just like a possibility - food for thought; or a thought experiment.
Secondly, the paragraph goes straight from "perceive a relation between two events without also perceiving the events themselves" to "we perceive both events as present", and on to "we must perceive them as simultaneous". It is totally unclear to me that everybody would read these assertions as facts or logically.
Generally, reading more of the article (the first introductionary paragraph), to be totally honest and opinionated, it seems weirdly flippant to me - there are many rhetoric questions in there, which does not seem quite up to the standard of other SEP articles I've read.
Later on, the article seems to become more earnest, but keeps being very open-ended. For example, the sentence:
But, arguably, we do not perceive events only, but also their temporal relations.
Indeed very arguable! While I of course don't know what objective reality is in this aspect, or how the brain works mechanically to represent time (nobody does), I can definitely think of different possibilities.
Having said all that, I can only assume that that article reflects the fact that the whole topic is wildly unknown. Nobody knows what time is, in a physical or philosophical sense; nobody knows what consciousness is or how it works; and nobody knows how the brain represents time mechanically, or how that information then enters consciousness.
So everything in this regard seems very opininon- and speculation-based to me; hence a SEP article with a lot of "ifs" and "maybes" and rhetoric questions with seemingly implicit answers. To answer questions like whether the "specious present" is a valid concept or even "objectively true" one would have to look elsewhere than this article.
The Wikipedia article on specious presence mirrors my sentiment - it seems obvious that something is going on here; but nobody seems to know anything for sure:
Finally, the claim of what precisely is being affirmed, in affirming the 'existence' of the specious present, is difficult to clarify. Philosophical theories of time do not usually interpret time to be in any unique way a production of human phenomenology, and the claim that we have some faculty by which we are aware of successive states of consciousness is trivially true.