I'm curious exactly what these people were experts in, because their reasoning and conclusions are deeply suspect. In order to fully address this question, I will first tackle historical documentation first, but will then expand more practically into my physical experience studying historical European martial arts.

This just isn't something you'll find evidence for in historical documents--and historical fighting manuals, like German language Fechtbücher, are essentially counter evidence. When they are illustrated, whether bucklers or shields are depicted as metal or wood is dependent on their size and what was popular at the time. Later period illustrations show more metal bucklers generally speaking. What's worth mentioning however, is that the descriptions of shield use and technique doesn't acknowledge this at all, suggesting the difference of shield material was not important. You can compare newer copies of older manuals and find identical text next to slightly different illustrations.

Broadly, the physics of what you were told is correct--wood generally absorbs impacts more than metal; it's why a wooden shield is easier to break that a metal one. The problem is that it assumes that this actually makes a great difference in the general context of fighting. When it comes to absorbing the impact from an opponent's strike, your bone structure is really the most important factor. Correct posture means that the structure of your skeleton will resist the impact--the shield just provides a striking surface for you to manipulate.

However because it's technically experimental archaeology, I believe this second half of the answer is really stepping outside of this board's focus. A better place to explore it would be r/wma.

Sources:

MS Dresd.C.487, Sächsische Landesbibliothek, Dresden, Germany

MS E.1939.65.341, Glasgow Museums, Glasgow, United Kingdom

MS M.I.29, Universitätsbibliothek Salzburg, Salzburg, Austria

Codex 44.A.8, Accademia Nazionale dei Lincei, Rome, Italy

MS 3227a, Germanisches Nationalmuseum, Nuremberg, Germany

And probably a few other manuscripts that I can't think of off hand.

Metal shields work. Otherwise people wouldn't have used them.

The problem with large metal shields is weight. If you have an all-metal shield (i.e., not metal over wood), you want the metal to be about 1mm thick or more, otherwise arrows will tend to go through it too easily. But a 36"/90cm diameter round shield would weigh about 5kg. A wooden shield of that size, covered in rawhide, and with a metal boss, might weigh about half of that - a big difference!

Arrows will tend to penetrate such a large-and-light wooden shield, but because the wood is elastic, it squeezes the arrow shaft as the arrow is going through, and there is a lot of friction and the arrow will usually be stopped before it gets to the all-too-delicate human body behind the shield. Swords will also cut into the rim of such shields, but this can be good thing, since it can trap the opponent's sword for long enough to hit them. These shields don't always last very long, and apparently fighters in formal duels could go through multiple shields as they were hacked to pieces.

The protection provided by iron/steel sheet improves quickly as it gets thicker, approximately quadratically. While 1mm thick is about the minimum that you'd want, when facing arrows, 2mm thick will be 4 times as protective, and will stop arrows reasonably reliably, and even stop most crossbow bolts. Conversely, making the iron/steel sheet thinner to reduce weight quickly makes it almost useless. So all-metal shields tend to be small. For a round shield 24"/60cm in diameter, a common size for cavalry round shields, one can have a shield 1.3mm thick for about 3kg, or go up to 2mm thick for about 4.5kg. A 12"/30cm buckler can be an almost invulnerable 3mm thick for well under 2kg.

Not all bucklers were metal. Some were rawhide (usually very thick), or wood (usually with iron parts as well). Iron/steel has the advantage of being more indestructible. Rawhide has the advantage of not rusting.

wood doesn't transfer the force into your arm like a metal shield would.

The force doesn't disappear. The force either damages the shield (which can be undesirable, even if not always), moves the shield (which works the same whether the shield is metal or wood), or is transferred to the user. Thick wooden shields which don't flex much or get damaged much will transfer just as much force to the user's arm as a metal shield.

Considering that metal plate armour works well, and a metal shield will be no worse than many pieces of metal plate armour for transferring force, this transfer of force shouldn't be a problem.

Also, arms are not that fragile, and a lot of weapons don't hit that hard. People block full-power punches with the arms without serious damage, and full-power kicks (which can hit much harder than many hand-help weapons) also usually (but not always) without serious damage.