I have a 1998 Yamaha U1.

Was told by the Yamaha in-house tuner that the double wound strings is the cause of the uneven tone (i.e. not full tone)production, which is the E-flat before middle C.

Nothing could be done to rectify this problem.

Could someone here confirm if it true ?

Most pianos have a change in tone at the wound strings to plain string change. It is difficult to even out the sound.

The piano being a U1 9 years old could use some extensive needling and will help even out the sound. Most techs don't like to because the Yamaha hammer are so hard they break needles. Offer to a good voicer to let him spend the time necessary to do the job right and you might like the results.

Wound strings are more massive than plain steel music wire- shorter pianos have more wound strings to provide lower pitched notes across shorter speaking lengths.

Big uprights, like the U7 have much smoother scales. The break point between wound and plain strings is bareley noticable. The U1 break is notorious- Yamaha technicians can not change the type of strings that are used- but they should be voicing the hammers to provide a smoother break.

On the U1, I believe the lowest plain wires are trichordal, whereas the adjacent wound strings are bichords. Greater sized pianos will either transition to bichordal plain wire notes, or switch to wound strings in the trichords; either solution provides a smoother break than you get on the U1.
However, for a 9 year old piano, I would also check the bridge and bridge pins, soundboard, and plate for cracking- any of which could affect the richness of tone in this area.

Only the lowest strings on a piano are double wound, and often not even them. They would be in the lowest octave of the piano. Most are single wound.

I assumed NW meant the bichord wound strings, which appear below middle C, instead of "double-wound" strings.
Here is a link to a measured U1H scale.
http://www.ptg.org/pipermail/pianotech/attachments/36/d0/40/23/YamU1H.jpg

Maybe nothing could be done warranty-wise - a smoother break is the benefit of the U3 over the U1.