I think what to leave for a tip in this type of situation depends very much upon the specific circumstances.
It's possible and perhaps even common for an otherwise fine server to provide poor service because of things going on in the restaurant that are out of his/her control. For example, if a bunch of large parties come in, or the kitchen is messing up orders, or the bar staff is being slow about drinks, or they're short-staffed--any of those things could cause a server to give poor service when, under other circumstances, the service would have been fine. Sometimes the customer can see stuff like that going on, and sometimes the customer is totally unaware of it.
The other thing to note is that comped items and extra attention from the manager shouldn't really be related to the tip to the server. The manager is just as motivated to comp things if the poor service is caused by restaurant-wide factors as he/she would be if the poor service is caused by the server alone. The goal for the manager is to get you to come back, and the free stuff is meant not to compensate you for the poor service (not exactly), but to leave you with a favorable impression of the restaurant as a whole. It's meant more to offset poor service than actually address it.
So I think the logic behind your BF's uncle's decision is not actually flawed (though I don't necessarily agree with his decision). The stuff provided by the manager is a separate issue than the tip, and shouldn't factor in. Where I would differ in his decision is that I try to give waitstaff the benefit of the doubt. Barring clear evidence that the server could have provided better service and just chose not to, and especially when there is clear evidence that the server was working against long odds, I generally assume the service they provided would have been acceptable under other circumstances, and leave at least my usual tip. I'm not going to punish the server for, essentially, fighting an losing battle they didn't create.
Even if the quality of service is within the control of the server, the comped stuff from the manager wouldn't matter. In that case, since the manager was showering me with free goods anyway, I would tell them that I thought the service was abysmal, and that I was not going to be leaving a tip because of it. The fact that they gave me some freebies might convince me to return to the restaurant in the future, but it wouldn't induce me to leave a tip that I thought was unwarranted. As a general rule, though, if I think the service is bad enough that I'm not inclined to leave at least my standard tip, then I need to make sure the manager knows about it. I don't leave less than 15% without saying something, because I can't guarantee otherwise that the message will be "the service stinks" and not "Dindrane is a stupid cheapskate."
I was actually in a somewhat similar situation recently, and I tipped what I normally would. We ended up with worse-than-usual service at a restaurant we go to regularly, but it was the end of the day and there was waitstaff clearly getting ready to end their shifts. Thus, the restaurant was somewhat short-staffed, and there was some pretty obvious confusion created by some people continuing to wait on customers while others were leaving.
So even though we had a hard time getting our server's attention, it was mostly because she was busy. We ordered drinks that we had to ask for again (because they forgot), and our food took forever, but it seemed to be a result of the general confusion. Someone who I think is the manager ended up helping to serve us, and he apologized for the service without us actually complaining about it. He also comped our drinks and gave us a coupon for a free appetizer the next time we went. I wouldn't always count the coupon as an acceptable response, but since we weren't actually planning to complain and were definitely planning on continuing to eat at the restaurant, we appreciated it. The overall experience ended up being a net positive, even though it did not start off all that well. The service provided by our actual waitress wasn't great, but it wasn't terrible and there were extenuating circumstances. So I gave her the benefit of the doubt and left my usual tip.
Plus, we like that restaurant and eat there a lot. I tip better at restaurants where I'm a regular, because if the waitstaff remembers me at all, I want it to be because I leave decent-to-good tips, not because I'm stingy.