No, this is not the same argument. It's an issue about the fundamental nature of the railway being used, and what that means to the underlying model - and it's based on what the law actually states.
Of course you can share capacity, if that capacity exists (and on peak summer days on many heritage railways, there's naff all spare). But if you want to run "big railway" trains at "big railway" speeds, you then bring in major costs to comply with "big railway" standards. That gives a double whammy of a) making a marginal cost operation have to fund investment and b) undermining the viability of the heritage railway. If that also undermines the local tourism sector, the effect is to undermine the whole local economy, not boost it. That needs thought, and it needs care.
We have an example, in reverse, of what you suggest - it's the NYMR between Grosmont and Whitby. The sharing significantly limits the flexibility of how NYMR can operate, while also constraining the scope of what could be done to boost Northern's service.
I also think the description of heritage railways as "playing trains" is a gross under-estimate of what they do - especially in tourist areas. These are important net contributors to the local economy