For context, I have been doing group rides for about 20 years now, raced at the cat 1/2 level for a good portion of that, and had a fixed gear obsession off and on for many years too. Riding fixed is an interesting challenge, but it is most certainly not an out and out advantage. The short of it is that your 55 kph fellow is likely a strong rider, who also knows how to time an impressive effort. The combination of the factors is leaving all of you scratching your heads and doubting yourself... club ride mission accomplished!
When fixed gear be an advantage
In the right circumstances fixed gear bikes can be extremely efficient. You have a straight chain line, no pulley wheels and a lighter overall bike. Plus, your momentum helps push the pedals through the dead spot, making it easier to spin fast. If your gearing is right for the stretch you are riding then you may actually be at an advantage. For example, if you have a flat time trial with consistent wind and the right top end gearing, once you are up to speed, you will be hard pressed to find faster set up (other than a full aero TT setup).
That said, fixed gear are only optimal in a limited set of situations... the rest of the time it's a suffer fest.
When fixed can be a giant disadvantage
While there are times you can fly on a fixed gear, depending on your environment and terrain it can also be a massive disadvantage. 55 km is a fast pace, which suggests he is pushing some big gear-inches. If you had any big climbs on your ride, or strong head winds, this gearing would likely be a massive suffer fest.
One of our club rides has attacks starting on a stretch with sustained 17 degree gradient. On a fixed gear with a tall gearing pretty much any rider would get tossed out the back due to the mechanical disadvantage.
We can also have some nasty sustained head winds. Again a fixed gear with tall gearing would be a suffer fest.
If you lowered the gearing to accommodate these features, you likely would be able to hit your 55 kph "chicken run" speed.
How to make yourself look stronger when at a disadvantage
One part of group riding is figuring out ways to turn the screws on your fellow riders. This is often a combination of psychological warfare and physical strength.
One of the best skills to learn is knowing your limits, your advantages, your disadvantages, and developing a good sense of timing. If I find myself at a disadvantage (i.e., slower bike, less fitness), I will focus on pacing, never doing more than the absolute minimum (conserve, conserve, conserve). I will likely plan for only one large effort, but in that effort I will put all my cards on the table (absolutely everything). Leave nothing behind (similar to the swimming scene in Gattaca. Even if that means getting spit out the back shortly afterwards.
All you need is one massive effort for everyone to remember and be intimidated. No one thinks that is all you have, they often assume you could do it again and again (which is often not the case).
What you can do
Next ride, watch him for the whole ride. Does he hold back on other aspects of the ride (like taking shorter pulls), allowing oneself to slip from the front to the back during climbs. Is your club ride fairly sedate before the "chicken run?" All of these scenarios may allow him to metering and conserve his effort in preparation for laying down a beating on your "chicken run."
If that is the case, it's not the bike that is the advantage its the combination rider and strategy and execution.
If you want to flip the situation, you need to play to your advantages and his disadvantages. Because you have gears, you can ride at an optimal gearing in more situations. You need to make use of this advantage. You can do this by attacking him whenever his fixed gear appears to be putting him at a disadvantage. If it looks like the his gearing is too tall on a climb, hammer the hell out of the climb. If you have a head wind, gutter the peloton so that he can't draft. The more you do this the more his fixed gear will become a liability, and the less reserves he will have left for the fabled "Chicken Run."