I think that the interpretation of the statement as extremely aristocratic lords looking down upon Queen Victoria and the royal family as persons of lower status is rather unlikely to be the correct one. Instead such statements more probably refer to her ability to keep in touch with the opinions of the middle class.
Many of the noble titles in England go far back into the Middle Ages. A popular saying at Arundel Castile is "Since William rose and Harold fell, there have been Earls of Arundel".
But the earldom of Arundell became extinct twice, before being created a third time in 1580 for the current line of Earls.
The oldest baron title of Ireland not held by someone with a higher title is the Barony of Kinsald (1340). The oldest baron of England not held by someone with a higher title is Baron de Ros (1288/89).
The Viscount Hereford (1550) is the oldest viscount title in the UK not held by someone with a higher title.
The Earl of Shrewsbury holds the oldest earldom in England not held by someone with a higher title, (1442), as well as the oldest Irish earldom, Waterford, (1446). The Earl of Crawford (1398) has the oldest Scottish earldom not held by someone with a higher title.
The Marquess of Winchester (1551) is the oldest Marquess title not held by a Duke.
The Duke of Norfolk (1453) has the oldest ducal title in the UK not held by a member of the royal family.
So no aristocratic family in the UK can claim to have been titled before those oldest titles were created, and most of them gained their titles in the Renaissance and modern eras.
In the Royal family of the UK, Prince Philip renounced his titles as a prince of Greece and Denmark when he married the queen. He - and all his descendants - is a member of the House of Schleswig-Holstein-Sonderberg-Glucksburg, which is a branch of the dynasty of Oldenburg. The family goes back in the agnatic (male only) line to Elimar I, Count of Oldenburg, who died in 1108. A German count had a much higher status than an English earl.
Queen Elizabeth II of the UK is descended in the agnatic line from Prince Albert, husband of Queen Victoria. Albert was a member of the House of Saxe-Coburg and Gotha, which ruled an independent country from 1806 to 1866. They are a branch of the House of Wettin, which goes back to Theodoric I, who died about 982. The house of Wettin became princes (high nobles) of the Holy Roman Empire when they acquired the Margravate of Meissen in 1089 and the Landgraviate of Thuringia in 1263. In 1423 the head of the family became one of the Electors of the Holy Roman Empire.
In about 1500, the royal families of Europe began to restrict their marriages to members of other royal families, except that they continued to intermarry with the princely dynasties of the Holy Roman Empire with their semi-royal status. So Queeen Elisabeth II's Wettin ancestors were much higher in status than any British nobles for centuries.
The only legitimate child of Emperor Frederick II to have descendants to the present time was a daughter Margaret, who married a Wettin, Albert II of Meissen. Their heir, by agnatic (male only) descent is Michael, Prince of Saxe-Weimer-Eisenach. And their heir general, allowing females to inherit if they have no brothers, is Queen Elizabeth II. So Elizabeth Ii could make a claim to be the rightful heir of the imperial Hohenstaufen and Salian dynasties, who claimed to be the rightful emperors of all the world. And when Duke Ernest II of Saxe-Corburg-Gotha died childless in 1893, Queen victoria's oldest son, the future Edward VII, became the heir general of the Hohenstaufen and Salian imperial dynasties, making Victoria a very close relative of that heir.
Queen Victoria herself was a member of the House of Hanover, a branch of the House of Welf or Guelf, which goes back in the agnatic line to Oberto I, Count Palatine of Italy, who died about 975. Members of the dynasty became dukes as early as 1070 and continuously from 1235, and the head of the dynasty became an Elector in 1692.
So the head of fhe House of Guelf had basically been a prince of the Holy Roman Empire, with a status almost equal to royalty, and much higher than English nobility, since about the time of origin of the earliest British titles of baron and earl that were still current in Queen Victoria's time.
So it would seem that Queen Victoria had a much more aristocratic background than even the oldest English aristocratic families.
The only families in Queen Victoria's United Kingdom who would have reason to look down upon her as some sort of parvenu of lower status than themselves would be some variously poor, middle class, and wealthy families of Celtic ancestry, descended from Irish and Welsh royal familes, whose ancestors had been overthrown and deposed by Saxon, Norman, and English invaders over the centuries.
Their ancestors had been kings for centuries before the first Hanoverian (1714), or Tudor (1485), or Stuart (1371 & 1603), or Plantagenet (1154), or Norman (1066), kings first ruled, and for centuries before the first known agnatic ancestors of those kings lived.
And their ancestors had been kings for centuries before the earliest known noble ancestors of Queen Victoria's Guelf dynasty.
A few of those families have acquired peerages, but such peerages, granted a thousand years perhaps after their ancestors were kings, have little to do with their origins in long ago royalty.
So I agree that the quotation is more about Queen Victoria's ability to keep in touch with the middle class than it is about British aristocrats thinking they were of higher status than the royal family.