I'm answering on direct painful experience on this one, having spent a lot of time under mine sorting it out.
I'm minded to agree with your welder at first glance, that looks fairly rotten, but as everyone else says, it's hard to tell from pics.
Here's the places you have to poke hard to see what's going on:
1. Inside sill edges where floor pan turns down and is spot welded on. Your underseal looks totally shot there. Probe all way along, from front to back of car.
2. Around all the rubber bungs, and d tabs. Again, your underseal is looking pretty worrying there.
3. All round the floor pans, rear in particular, but also fronts at sill edges.
4. Boot floor pan.
5. While you're in the mood, take the back wheels off and poke about the bodywork facing you, as well as the arch inner skins, petrol filler neck, clips, and body mounting point.
Also, use a Stanley knife to knick any bubbles. If they weep water, you're probably in trouble.
The thing about the punto factory underseal (probably like many other cars) is that it is quite rubbery, and looks passable when in fact it's had it.
Btw, forget using a hand wire brush, you'll be there for ever. Get an angle grinder with a twisted knot wire wheel on it. Just watch your car disappear....
Gloves, good goggles, ear defenders and I use a good quality p3 halfmask otherwise you'll have every facial orifice full before you know it
yep they did but i pealed these back a bit to inspect the metal and its solid, so why would i be in troublee, and i have inspected those listed areas and all good,