Well, yes, I think it is generally known that Beethoven did in fact use "high notes" in his early and late string quartets. Not to mention low and middle ones. So to test this odd claim, let's just have a look at those supposedly indicative middle-period quartets, op 74 and op 95, the 'Harp' and 'Serioso' quartets. On page 2 of the score of the 'Harp' quartet the first violin ascends to the fifth ledger line above the staff. On the next page, to the space above the fifth ledger line, on page four to the space above the fourth ledger line, on page five to the fifth ledger line again and so on. The Quartet op 95 shows the same kind of tessitura in the first violin. These are high notes. Very high notes. The same kind of high notes that we find in the early and late quartets. Neither I nor any other musicologist over the last 200 years have noticed any avoidance of high notes in the middle-period music of Beethoven and I sure don't see it in the scores.Researchers from the University of Amsterdam, have found his early quartets (opus 18, 1798-1800) used a variety of high notes.Beethoven, who suffered from a severe form of tinnitus, first mentioned his hearing problems in 1801 in a letter to Franz Wegeler and Karl Amenda.He wrote: "In the theatre I have to get very close to the orchestra to understand the performers, and that from a distance I do not hear the high notes of the instruments and the singers' voices."By 1810, when he composed the opus 74 and 95 quartets, the amount of high notes he used dropped significantly, tending towards lower frequency notes.But the higher registers increased again in 1825, when he wrote the late string quartets opus 127 to 135 and it was thought he had become completely deaf.The report's author Edoardo Saccenti said: "These results suggest that, as deafness progressed, Beethoven tended to use middle and low frequency notes, which he could hear better when music was performed, seemingly seeking for an auditory feedback loop."When he came to rely completely on his inner ear he was no longer compelled to produce music he could actually hear when performed and slowly returned to his inner musical world and earlier composing experiences."
Now, to be fair, I haven't seen the original article with its research data so perhaps I am missing something. But one thing is for sure: the BBC is shining everyone on with this ridiculous balderdash. Here's a tip: don't believe anything you read in the paper, hear on the radio or see on TV, especially when it makes some kind of scientific claim. The kind of 'science' we get in the mass media is absurdly over-simplified when it isn't utterly mistaken.
Here is the first movement of the Quartet op 74. Have a listen for the high notes, the first of which occur around 2:24 to 2:27: