I my experience only 2 or 3 passengers are lost at each tender port. Given that there are 2000 or more passengers, to lose 6 or 7 per cruise is not a lot.
I'm sorry, I needed to write that.
Most of the time tendering is a smooth process that works like this.
Once you are ready to get off the ship you proceed to an area where they give out tender tickets. This ensures a smooth flow of pasengers towards the tender area . You usually proceed to a lower deck where there is usually a stairscase outside the ship. At the bottom of the staircase there is a platform, about 8 x 12 feet . There will be several ships crew members to assist you in the orderly stepping accross to the tender.
If seas are calm the tender will be tied tight to the platform and you will simply step accross (no gap) . There will be a crew member holding your hand on the platform and another to take your hand when you step accross. If seas are a bit rough, you may have to time your step, but, at no time are you steppng accross or jumpng accross a giant gap between the ship and tender. I have seen elderly, handicapped , folks in wheel chairs, with walkers, canes and crutches get on and off the tender. The ship is not going to risk your safety. There is definately no leaping accross large open gaps. Not all passengers are Jackie Chan.
Shore side since there is usually no movement of the water the tender is usually tied tight against the dock and sometimes there is a dock plate or step put between.
I'm not sure who wins the bet, I'd say split the difference and spend the $ 50 on tequilla and cervesa in Cozumel.
Have no fear, you will be fine. If Gram can do it, anybody can do it.