The whole argument of "can't deal with 1000 web users at a time" is a chimera. If you truly had 1000 users slamming an ORACLE back-end at the same time, it would exhibit performance issues, too. Just not as bad as Access-to-Access traffic. Not to mention that Larry Ellison started switching his product to the "per thread" licensing scheme just before I retired...
Access and a web-based front-end with an ORACLE back end would have the same capacity of DB threads. The difference isn't anything more or less than having a connection protocol difference. That difference is that when you connect via a desktop running an Access front-end, you have licensing fees for the Access product - and I believe you could distribute an Access Run-Time engine for which there would be no such fees.
The next difference is whether you authenticate to a domain controller or a RADIUS server (for desktop Access) or whether the authentication is done within the host of the database because the web is just a pass-through connection.
Then you would wonder whether the database services are part of a cluster that does shared data locking cross-cluster in order to get high volume and high availability. That is a function of the connection design, not of Access or ORACLE or SQL Server.
Saying that Access doesn't work so well for big apps is in part due to forgetting that there IS such a thing as having a heterogeneous database with an Access FE and something else for the BE. All of the problems with concurrent users are governed by the BE's capacity, and if Access is only the FE, that 255-user limit ain't there no more.
The REAL reason that IT folks don't like Access FE is when they have Access BE, the SMB protocol used by Windows file sharing is a nightmare both for security and for the implied volume of traffic it engenders, since a query has to process the entire table on the FE and that means reading the entire table from the BE.
If you could set up that split FE/BE to be heterogenous and use pass-through queries to be processed on the BE and see only the results on the FE, Access is no worse than any other system.