Here are some sources I found:

1989 court case

The main legal case is the Apple Computer, Inc. v. Microsoft Corp. 1989, where the change from tiling window management to overlapping was an important aspect. However, this is after the change had already been done, so it may not have been significant in the original decision to use a tiling manager. The court case may have distorted later reporting about the Windows 1 vs. 2 design decisions.

Info World 1983

The Info World magazine November 21, 1983 contains a statement by “Steve Bulmer” _[sic]:

But Microsoft has chosen a “tiling” approach to windowing. In a tiling approach, the screen display is divided into columns, and the columns are broken into windows. Windows has a built-in “automatic window layout” feature that resizes all the windows when the size of any one window is altered, so that the windows never overlap. When one window is placed on top of another window, the covered window is instantly transformed into a pictorial representation or icon, and displayed at the base of the screen.

“It’s the metaphor of the neat desktop,” said Steve Bulmer, Microsoft vice-president for marketing. He said that after an extended internal debate about the philosophy of designing window managers, Microsoft had settled on a user interface that will handle many window-sizing functions automatically.

Bulmer claimed that the tiled approach to windowing is a more intuitive and predictable user interface. He says that a user can change window size or position with a single mouse click.

Info World 1987

The Info World magazine April 6, 1987 reports that the change to overlapping windows would be a result of the OS/2 collaboration with IBM:

Windows 2.0 to Resemble OS/2 Windows Manager

Microsoft has launched an effort to transform the appearance of the control software. The firm announced last week it would make available a new version of Windows, called Version 2.0, in the third quarter that would have a new visual appearance identical to the OS/2 Windows Presentation Manager.

The new appearance is the result of a development agreement between Microsoft and IBM, and the main difference is that windows now overlap instead of “tile.” Windows 2.0 offers the same external appearance as the Windows Presentation Manager, but it’s compatible with the existing applications and device drivers written for the current Windows.

Technical capability

I initially expected that there could have been technical limitations such as inability to interact with the windows underneath the popup window.

But that appears to not be true, as I have tried myself with the “Cardfile” popups in online emulator.
They are fully movable, can overlap other tiled applications and the windows underneath can be interacted with. They are not resizable, but that is probably an application choice for dialogs.

PC Magazine 1984

The PC Magazine June 12, 1984 notes that the technical capability is present:

Although I said earlier that Microsoft has used window tiling to display multiple sources of information simultaneously, the truth is that tiling is only the preferred technique. If software developers wish to employ windows that overlap, then they may do so. If developers wish to employ Macintosh-style windows (but not icons), they may also do so. However, Microsoft has included all the necessary code to draw standard Microsoft windows if developers include the right calls in their applications.

Conclusion

These sources align with the BetaWiki claim that the tiling was a design decision rather than legal or technical limitation.

It could have made more sense at the time when you consider how many Microsoft users would have been unfamiliar with GUIs and mouse usage. The tiling windows as implemented by Windows 1.0 offer less chances for confusion, such as losing a non-minimized window behind another window. Remember that the innovation of the task bar that shows all open windows came much later with Windows 95.