The essential premise of this idea is that, in order:

Charlemagne was crowned emperor in 800, but the title fell into disuse as his empire fractured following his death; it was revived by Otto I fashioned himself the Holy Roman Empire in 962, but the situation was much changed and the empire and papacy often came into conflict thereafter, as with Gregory VII and Henry IV's conflict in which each sought to depose the other.

Although it was sanctioned by the pope in Rome (if we take Charlemagne's coronation as a starting point for the HRE), the empire was Frankish, not Roman; the empire which traced descent from the Roman Empire was the Byzantine Empire, which still existed at the time; hence, the HRE can be said to have not been Roman.

The fact of the empire was that although there was a nominally elected ruler, in practice he ruled over a large collection of city-states, princes, kingdoms and dukes, many of which he only ruled over nominally. In this sense, the HRE was not an empire in that it can be seen more as a collection of states under the nominal leadership of the emperor.

The trope began as a quote from Voltaire, famous French satirist. At the time he said it, late 18th cent. It was quite accurate and very funny because it poked holes at the long dead premise for this empire and its absurd title. It was not holy, of course, almost any institution at this time was not really holy. It had almost nothing to do with Rome at this point although originally it was supposed to be sort of follow up to that.

And while technically it was an empire as there were separate kingdoms, it was horribly broken up, or "balkanized" into so many parts that were not contiguous to one another. Also the crazy patchwork of various, duchies, knight, ecclesiastical entities that all formed this strange empire.

so the quote was quite n the mark. Not sure what you mean by "how accurate is it to say that?" The empire is long gone, it no longer exists in the present, it was dissolved by Napoleon.