I saw a picture of a fighter in the UK in a Muay Thai match reach down to catch the leg of the opponent throwing a kick to his thigh. I was once told that this is not advisable. In the move as he reached down grabbing the leg, he threw a punch from the other side.
Is grabbing kicks lower than the waist advisable? Are there particular situations where it is or isn't?
Anderson Silva, an MMA fighter with a muay Thai background, has executed low-kick catches in the UFC against Chael Sonnen (to an inside leg kick, no less) and James Irvin, as described in this Judo Chop article. The James Irvin kick catch was simply spectacular, and seems like it would apply well to strict MT competition as well. (Note that the Irvin kick looks like it's to the hip, but that's because Silva changed levels in order to better catch the kick.) So it seems that there are definitely situations where catching the kick is a reasonable choice.
Whether attempting a low-kick catch is advisable generally is an open question. Since it requires changing levels and has less chance of working than a middle or high kick catch, it might reasonably be considered a less viable technique or appropriate in fewer situations.
If the kick is slow enough or sloppy enough to be caught, then yes you should catch it. Why not - it's there for the taking. In a non-tournament situation (i.e. real life) catching a kick should mean fight over.
When shouldn't you catch a kick? When you run the risk of breaking your arm by getting it in the way, or you become vulnerable to further techniques (punches, a clinch) because you've dropped your guard.
Catching a kick below waist level is not easy and would normally be the result of the opponent making a mistake rather than a deliberate strategy. It's not commonly seen in Muay Thai because most practitioners are actively taught how not to kick, which minimises the chances of the kick being caught.
As for the specific picture you saw - I'm surprised that the fighter threw a punch. Catching the kick is a great setup for a sweep or countering thigh kick, or even a knee to the rib or inside thigh of the held leg - all of which are point scoring opportunities in traditional Muay Thai.
