can overfilling with oil stop a lawnmower from starting?

I have a Brigg & Stratton 875 series. A few weeks ago it just refused to start. After priming it would give a cough and a puff of smoke - no start- no further reactions to pulling the string thing.

It was new in October 2008 so I took it back to supplier, they say the problem was overfilling with oil so a non-warranty charge was made.

I put more oil in at the beginning of summer and it ran for 2-3 months ok before refusing to start.

Am I right to suspect their analysis of the problem is dubious?