'Corroborate' refers more to supporting something with evidence. You are making something more certain, or adding authority to a statement. For example "Recent research seems to corroborate his theory". I think your example is ok because you are talking about research/evidence supporting a view. 'Support' can be used in this context - "Recent research seems to support his theory". However, it can be used in contexts where there is no research/evidence. You can support your friend in an argument simply because you are his friend. You can support an idea without having evidence to 'back it up'. You can support a football team without providing any information as to why.

"I could not corroborate his story." You could use it as a synonym for support, but it depends on the context. It is typically used to mean [to confirm]. Hope this helps. Lacei