Suzanne, no need to assume. I'm pretty sure those two persons made it clear the browser was *part of the job scope*.
I understand *a browser* is the only way you can do your work, as a matter of fact that's what the OP (Mark K) implied for himself when he said "This makes web development very challenging lol." (referring to not using a browser; note that he is a web developer).
If it happened to two persons it's enough to create a precedent, it doesn't need to happen to all of us .
And yes, I'm going to take their word for it, I don't see any reason why people with pretty solid work history/feedback would make up stories like that.
As for "being up to the Client what they think is appropriate or not" - no.
I would leave that to a well trained, impartial person (or persons) that can take their time and make an objective decision based on the job requirements/discussions/specs/whatever. Having an (obviously) unsatisfied client filing a dispute decide what's appropriate or not - not cool.