The unattributed quote you pasted says "breastfed" not "exclusively breastfed". So it's not saying that the occasional bottle makes kids more susceptible to allergies. And it's certainly not saying that cows' milk "can be a trigger for allergies"; drinking cows' milk proteins won't trigger, for example, a shellfish allergy.
But, hey, let's think about if your claim is even reasonable. There are a number of things to consider and I'm going to go through some of them.. because the lack of critical thinking about things like this is one of my pet peeves.
First, why breastfeed? One of the big reasons for breastfeeding is that the maternal antibodies protect the child from infection and perhaps allergies. We'll take that as a given and I will fully agree here that "breast is best". Now, the question is, how long do those antibodies persist? Are they so transitory that skipping one feed makes a child appreciably more susceptible to infection and allergies? My guess is no. If that were true, many things need to be rethought about feeding (eg, an infant should be fed every x hours day and night and woken up if she is sleeping too long ). So skipping a feed is not going to effect the chances of having allergies.
The next question becomes, does formula in and of itself cause allergies? I'm only going to talk about the specific case of giving a bottle every now and then. The maternal antibodies, as mentioned before, are still in full force. Food allergies are mediated by IgE (for the immediate symptoms) and IgG (delayed symptoms); I say this like it's clear cut, but it's not. A child can have high levels of IgE and not react to a food (my son's RAST showed more chicken IgE than milk and he's fine with chicken). Your position seems to be that too much cows' milk (because, as I've previously mentioned, there is cows' milk in a woman's breastmilk if she has dairy) can cause an allergy (which is different than causing a reaction because a reaction does depend on amount, but it's mainly dependant on having the allergy in the first place). Let me emphasize the fact that exposure to the particular food protein is necessary for the allergy to develop.. a child is not going to be allergic to a food he hasn't been exposed to. Ok, rambling a bit, but you seem to be saying that too much cows' milk can cause a cows' milk allergy. Is this true? No. It's simply not. It's not the amount, it's the exposure that is necessary for the allergy. Repeated exposure builds up the allergy (a doctor explained it to me as "tickling" the allergy). Anyway, if you want to argue this point, that's fine.
To sum up: breastmilk is useful to help prevent allergies because it contains substances which do something to a child's immune system to make him less susceptible. These substances most likely don't disappear if the occasional feed is missed, so the child still has protection. Formula in and of itself won't cause an allergy. And to repeat myself again, I'm talking about the specific case of giving formula every once in a while.
Now, all that is not to say that formula won't cause more of a reaction if a child has an allergy, especially if it has more cows' milk than the mother's breastmilk. While a small amount of a food can provoke a horrible reaction, it's generally true that in each particular instance more of that food is worse. (It's more complicated than that, of course. Allergies are weird.)
So why do some studies say "exclusive breastfeeding" helps protect against allergies? Most likely it's because exclusive breastfeeding means just that : no formula whatsoever. Easy to measure, easy to control who gets put in what group: exclusive breastfeeders and formula feeders. The latter group would contain mothers like barlow, mothers who replace one feed a day with formula, mothers who breastfeed, but send their kids to nursery with formula and mothers who don't breastfeed at all. Each of those subgroups is different. Barlow's child will have effectively the same amount of maternal antibodies as the exclusive breastfeeders and she is not repeatedly exposing her child to cows' milk protein via the formula. The mother who replaces one feed a day with formula will have a child who has 1/6 less maternal antibodies than she would have if exclusively breastfed (that's making a number of assumptions, of course, the main two being that maternal antibodies go linearly with number of breastfeeds and that it actually will make a difference -- both are huge assumptions). And so on... So even studies that differentiate between full time formula feeders and those mothers that breastfeed some are inapplicable here.
So, in conclusion (finally!) I think it's just wrong to lay guilt on someone for this.