He's probably right. The character was credited as "Doctor Who" for the first eighteen seasons and then again for Eccleston's series. It's hard to argue against the programme's own credits.

I used to get annoyed about new fans referring to each multi-episode original series story as an 'episode' (singular) or 'arc' (e.g. "my favourite episode is Genesis of the Daleks" or "The Ribos Operation is an under-rated arc"), but eventually I realised that I was probably trying to gate-keep. Although the pedant in me still gets annoyed sometimes.